12.1. Simple Harmonic Motion (SHM)

Cards (96)

In SHM, the velocity of an object is maximum at the midpoint
Arrange the conditions for SHM in the correct order:
1️⃣ Restoring force is proportional to displacement
2️⃣ Restoring force is directed towards equilibrium position
3️⃣ No external forces other than restoring force
In the equation for SHM, what does $\omega$ represent? 
Angular frequency
In SHM, the period is the time taken for one complete oscillation
The number of oscillations per unit time in SHM is called frequency
The acceleration in SHM is always directed towards the equilibrium position. 
True
In SHM, the acceleration of an object is proportional to its displacement and directed towards a fixed point. 
True
SHM contrasts with uniform circular motion in the relationship between acceleration, velocity, and displacement.
True
The equation for acceleration in SHM is $a =$ $- \omega^{2} x$
What does the amplitude in the displacement-time graph represent?
Maximum displacement
The period in SHM is constant. 
True
Simple Harmonic Motion (SHM) is a type of oscillatory motion where the acceleration is proportional to its displacement
In SHM, the velocity is maximum at the midpoint
The restoring force in SHM must always be directed towards the equilibrium
Steps in deriving the SHM equation using Newton's Second Law and Hooke's Law:
1️⃣ $ma =$ $- kx$
2️⃣ $a =$ $- \frac{k}{m}x$
3️⃣ $\omega^{2} =$ $\frac{k}{m}$
4️⃣ $a =$ $- \omega^{2} x$
What does the period of the displacement-time graph in SHM represent?
One complete oscillation
What does the amplitude in the displacement-time graph represent?
Maximum displacement
What is the direction of acceleration in SHM in relation to displacement?
Towards equilibrium
What does the sinusoidal shape of the displacement-time graph reflect in SHM?
Periodic and repeating motion
Where is the velocity zero in SHM?
Maximum displacement points
The equation for acceleration in SHM is $a =$ $- \omega^{2} x$ , where $\omega$ is the angular frequency
Match the graphs in SHM with their corresponding properties:
Displacement-Time ↔️ Displacement varies sinusoidally
Velocity-Time ↔️ Velocity is maximum at midpoint
Acceleration-Time ↔️ Acceleration is proportional to displacement
In SHM, the equation relating acceleration and displacement is a = - ω²x
What is the definition of amplitude in SHM?
Maximum displacement
In SHM, the period is dependent on the amplitude.
False
In SHM, the restoring force must always be directed towards the equilibrium position. 
True
Steps to derive the equation for SHM using Newton's Second Law and Hooke's Law
1️⃣ ma = - kx
2️⃣ a = - (k/m)x
3️⃣ Substitute ω² = k/m
4️⃣ a = - ω²x
Newton's Second Law is expressed as $F =$ $ma$ , and Hooke's Law is $F =$ $- kx$ , where $k$ is the spring constant
In the SHM equation a = - \omega^{2} x</latex>, $\omega$ represents the angular frequency
Match the features of the displacement-time graph in SHM with their descriptions:
Amplitude ↔️ Maximum displacement from equilibrium
Period ↔️ Time for one complete oscillation
Frequency ↔️ Number of oscillations per unit time
In SHM, the period of oscillation is constant
In SHM, the velocity is zero at the extremes of motion. 
True
In Simple Harmonic Motion, the acceleration is always directed towards the equilibrium position.
The acceleration in SHM is maximum at the midpoint of the motion.
False
The equation for the period in SHM is $T =$ $\frac{1}{f}$ , where $f$ is the frequency.
In SHM, the total energy of the system remains constant.
True
A mass-spring system is an example of SHM. 
True
What type of motion is Simple Harmonic Motion (SHM)?
Oscillatory motion
Match the characteristic of SHM with its description:
Acceleration ↔️ Proportional to displacement, directed towards fixed point
Velocity ↔️ Maximum at midpoint, zero at extremes
Displacement ↔️ Sinusoidal, repeating pattern
Period/Frequency ↔️ Constant, independent of amplitude
What is the defining characteristic of SHM related to acceleration and displacement?
Proportionality