Oscillation

• A mass-spring system on a horizontal frictionless surface is set in simple harmonic motion with amplitude A. The mass is then doubled and the system is again set into simple harmonic motion with the same amplitude. Which of the following is true about the total mechanical energy of the system due to doubling the mass?

  a. It has doubled.

  b. It has quadrupled.

  c. It has halved.

  d. It has not changed.

  d
• If a long spring with spring constant k is cut into 4 equal lengths, what is the spring constant of each of the 4 shorter springs?

  a. It is still k.

  b. It is k/4.

  c. It is 4 k.

  d. It is k/16.

  c
• When an object is moving in simple harmonic motion, which of the following is at a minimum when the displacement from equilibrium is zero?

  a. the magnitude of the velocity

  b. the magnitude of the acceleration

  c. the kinetic energy

  d. the total mechanical energy

  b
• A pendulum on the Earth has a period T. The acceleration of due to gravity on Mars is less than that on the Earth, and the acceleration due to gravity on the Moon is even less. Where would the period of an identical pendulum be the least?

  a. on the Earth

  b. on the Moon

  c. on Mars

  d. The period of a pendulum would be the same on the Earth, Moon, and Mars since the

  period depends on the pendulum's length which is the same for identical pendula.


  a
• Two identical springs, each with spring constant k, are attached in parallel to a mass, which is then set into simple harmonic motion. What would be the spring constant of a single spring which would result in the same frequency of oscillation as the parallel springs?

  a. k

  b. 2k

  c. k/2

  d. k

  b
• The SI base units for spring constant are which of the following?

  a. kg·s2

  b. kg/m2

  c. kg/s2

  d. kg·m2

  c
• A large spring requires a force of 150 N to compress it only 0.010 m. What is the spring constant of the spring?

  a. 125 000 N/m

  b. 15 000 N/m

  c. 15 N/m

  d. 1.5 N/m

  b
• A 0.20-kg object is attached to a spring with spring constant k = 10 N/m and moves with simple harmonic motion over a horizontal frictionless surface. At the instant that it is displaced from equilibrium by −0.050 m, what is its acceleration?

  a. 1 000 m/s2

  b. −40 m/s2

  c. 0.1 m/s2

  d. 2.5 m/s2

  d
• Tripling the weight suspended vertically from a coil spring will result in a change in the displacement of the spring's lower end by what factor?

  a. 0.33

  b. 1.0

  c. 3.0

  d. 9.0

  c
• Tripling the displacement from equilibrium of an object in simple harmonic motion will bring about a change in the magnitude of the object's acceleration by what factor?

  a. 0.33

  b. 1.0

  c. 3.0

  d. 9.0

  c
• A tiny spring, with a spring constant of 1.20 N/m, will be stretched to what displacement by a 0.005 0-N force?

  a. 4.2 mm

  b. 6.0 mm

  c. 7.2 mm

  d. 9.4 mm

  a
• A mass of 0.40 kg, attached to a spring with a spring constant of 80 N/m, is set into simple harmonic motion. What is the magnitude of the acceleration of the mass when at its maximum displacement of 0.10 m from the equilibrium position?

  a. zero

  b. 5 m/s2

  c. 10 m/s2

  d. 20 m/s2

  d
• A mass of 4.0 kg, resting on a horizontal frictionless surface, is attached on the right to a horizontal spring with spring constant 20 N/m and on the left to a horizontal spring with spring constant 50 N/m. If this system is moved from equilibrium, what is the effective spring constant?

  a. 30 N/m

  b. -30 N/m

  c. 70 N/m

  d. 14 N/m

  c
• Suppose there is an object for which F = +kx. What will happen if the object is moved away from equilibrium (x = 0) and released?

  a. It will return to the equilibrium position.

  b. It will move further away with constant velocity.

  c. It will move further away with constant acceleration.

  d. It will move further away with increasing acceleration.

  d
• If it takes 4.0 N to stretch a spring 6.0 cm and if the spring is then cut in half, what force does it take to stretch one of the halves 3.0 cm?

  a. 2.0 N

  b. 4.0 N

  c. 8.0 N

  d. 16 N

  b
• Three identical springs each have the same spring constant k. If these three springs are attached end to end forming a spring three times the length of one of the original springs, what will be the spring constant of the combination?

  a. k

  b. 3 k

  c. k/3

  d. 1.73 k

  c
• A 0.20-kg object is oscillating on a spring with a spring constant of k = 15 N/m. What is the potential energy of the system when the object displacement is 0.040 m, exactly half the maximum amplitude?

  a. zero

  b. 0.006 0 J

  c. 0.012 J

  d. 2.5 J

  c
• A 0.20 kg object, attached to a spring with spring constant k = 10 N/m, is moving on a horizontal frictionless surface in simple harmonic motion of amplitude of 0.080 m. What is its speed at the instant when its displacement is 0.040 m? (Hint: Use conservation of energy.)

  a. 9.8 m/s

  b. 4.9 m/s

  c. 49 cm/s

  d. 24.5 cm/s

  c
• A mass of 0.40 kg, hanging from a spring with a spring constant of 80 N/m, is set into an up-and-down simple harmonic motion. What is the speed of the mass when moving through the equilibrium point? The starting displacement from equilibrium is 0.10 m.

  a. zero

  b. 1.4 m/s

  c. 2.0 m/s

  d. 3.4 m/s

  b
• A mass of 0.40 kg, hanging from a spring with a spring constant of 80 N/m, is set into an up-and-down simple harmonic motion. What is the speed of the mass when moving through a point at 0.05 m displacement? The starting displacement of the mass is 0.10 m from its equilibrium position.

  a. zero

  b. 1.4 m/s

  c. 1.7 m/s

  d. 1.2 m/s

  d
• A runaway railroad car, with mass 30 × 104 kg, coasts across a level track at 2.0 m/s when it collides with a spring-loaded bumper at the end of the track. If the spring constant of the bumper is 2.0 × 106 N/m, what is the maximum compression of the spring during the collision? (Assume the collision is elastic.)

  a. 0.77 m

  b. 0.58 m

  c. 0.34 m

  d. 1.07 m

  a
• A 0.20-kg mass is oscillating on a spring over a horizontal frictionless surface. When it is at a displacement of 2.6 cm for equilibrium it has a kinetic energy of 1.4 J and a spring potential energy of 2.2 J. What is the maximum speed of the mass during its oscillation?

  a. 3.7 m/s

  b. 4.7 m/s

  c. 6.0 m/s

  d. 6.3 m/s

  c
• A 0.20-kg block rests on a frictionless level surface and is attached to a horizontally aligned spring with a spring constant of 40 N/m. The block is initially displaced 4.0 cm from the equilibrium point and then released to set up a simple harmonic motion. What is the speed of the block when it passes through the equilibrium point?

  a. 2.1 m/s

  b. 1.6 m/s

  c. 1.1 m/s

  d. 0.57 m/s

  d
• A 0.20-kg block rests on a frictionless level surface and is attached to a horizontally aligned spring with a spring constant of 40 N/m. The block is initially displaced 4.0 cm from the equilibrium point and then released to set up a simple harmonic motion. A frictional force of 0.3 N exists between the block and surface. What is the speed of the block when it passes through the equilibrium point after being released from the 4.0-cm displacement point?

  a. 0.45 m/s

  b. 0.63 m/s

  c. 0.80 m/s

  d. 1.2 m/s


  a
• Suppose a 0.3-kg mass on a spring that has been compressed 0.10 m has elastic potential energy of 1.0 J. How much further must the spring be compressed to triple the elastic potential energy?

  a. 0.30 m

  b. 0.20 m

  c. 0.17 m

  d. 0.07 m

  d
• Suppose a 0.30-kg mass on a spring-loaded gun that has been compressed 0.10 m has elastic potential energy of 1.0 J. How high above the spring's equilibrium point can the gun fire the mass if the gun is fired straight up?

  a. 0.10 m

  b. 0.34 m

  c. 0.24 m

  d. 10 m

  c
• An object is attached to a spring and its frequency of oscillation is measured. Then another object is connected to the first object, and the resulting mass is four times the original value. By what factor is the frequency of oscillation changed?

  a. 1/4

  b. 1/2

  c. 1/16

  d. 4

  b
• By what factor must one change the weight suspended vertically from a spring coil in order to triple its period of simple harmonic motion?

  a. 1/9

  b. 0.33

  c. 3.0

  d. 9.0


  d
• Which one of the following quantities is at a maximum when an object in simple harmonic motion is at its maximum displacement?

  a. speed

  b. acceleration

  c. kinetic energy

  d. frequency

  b
• A mass on a spring vibrates in simple harmonic motion at a frequency of 4.0 Hz and an amplitude of 8.0 cm. If the mass of the object is 0.20 kg, what is the spring constant?

  a. 40 N/m

  b. 87 N/m

  c. 126 N/m

  d. 160 N/m

  c
• For a mass suspended on a spring in the vertical direction, the time for one complete oscillation will depend on:

  a. the value for g (the acceleration due to gravity).

  b. the distance the mass was originally pulled down.

  c. the maximum speed of the oscillating mass.

  d. the time doesn't depend on any of the above.

  d
• A mass on a spring vibrates in simple harmonic motion at a frequency of 4.0 Hz and an amplitude of 4.0 cm. If a timer is started when its displacement is a maximum (hence x = 4 cm when t = 0), what is the speed of the mass when t = 3 s?

  a. zero

  b. 0.006 5 m/s

  c. 0.015 m/s

  d. 0.024 m/s

  a
• A mass on a spring vibrates in simple harmonic motion at a frequency of 4.0 Hz and an amplitude of 4.0 cm. If a timer is started when its displacement is a maximum (hence x = 4 cm when t = 0), what is the acceleration magnitude when t = 3 s?

  a. zero

  b. 8.13 m/s2

  c. 14.3 m/s2

  d. 25.3 m/s2

  d
• An object moving in simple harmonic motion has an amplitude of 0.020 m and a maximum acceleration of 40 m/s2. What is the frequency of the system?

  a. 0.60 Hz

  b. 51 Hz

  c. 7.1 Hz

  d. 16 Hz

  c
• The position of a 0.64-kg mass undergoing simple harmonic motion is given by

  x = (0.160 m) cos (πt/16). What is its period of oscillation?

  a. 100 s

  b. 32 s

  c. 16 s

  d. 8.0 s

  b
• The position of a 0.64-kg mass undergoing simple harmonic motion is given by

  x = (0.160 m) cos (πt/16). What is the maximum net force on the mass as it oscillates?

  a. 3.9 × 10-3 N

  b. 9.9 × 10-3 N

  c. 1.3 × 10-3 N

  d. 6.3 N

  a
• The position of a 0.64-kg mass undergoing simple harmonic motion is given by

  x = (0.160 m) cos (πt/16). What is its position at t = 5.0 s?

  a. 0.160 m

  b. 0.159 m

  c. 0.113 m

  d. 0.089 m

  d
• its maximum value when the displacement from equilibrium is at what point in its swing?

  a. zero displacement

  b. 1/4 the amplitude

  c. 1/2 the amplitude

  d. equal the amplitude

  a
• A simple pendulum has a period of 2.0 s. What is the pendulum length? (g = 9.8 m/s2)

  a. 0.36 m

  b. 0.78 m

  c. 0.99 m

  d. 2.4 m

  c
• A simple pendulum has a mass of 0.25 kg and a length of 1.0 m. It is displaced through an angle of 30° and then released. After a time, the maximum angle of swing is only 10°. How much energy has been lost to friction?

  a. 0.29 J

  b. 0.65 J

  c. 0.80 J

  d. 1.0 J

  a