Simple Harmonic Motion

• Simple harmonic motion (SHM) occurs when an object moves in such a way that its acceleration is always directed toward a fixed point and is proportional to its distance from the fixed point, represented by the equation a=-w2x.
• In the case of SHM, the object is displaced and then released so that it oscillates vertically.
• At its maximum displacement, the force from the spring causes the mass to accelerate upwards towards the equilibrium position.
• If the object is released at its maximum displacement and the stop clock was started at the same time as the object was released, ε=0 radians, therefore t=0, cos(ωt) = 1 and therefore x=A.
• When the stop clock is started at a different point in the cycle, ε will not be equal to 0.
• If the object is moving through the equilibrium position towards the maximum positive displacement at t=0, then ε=−2π.
• Both ω and ε are measured in radians, therefore your calculator must be set in radians mode before you use the cos and sin functions.
• The corresponding equation for the velocity of the object is:v=-Aω sin(ωt+ε).
• The minus sign in the equation ensures that v is negative initially as it moves away from the point of maximum positive displacement and is positive as it moves away from the maximum negative displacement.