Question

The displacement in simple harmonic motion is a maximum when theA) acceleration is zero. D) kinetic energy is a maximum.B) velocity is a maximum. E) potential energy is a minimum.C) velocity is zero.

Answer 1

C) velocity is zero.

Step-by-step explanation:

In a simple harmonic motion, the total mechanical energy of the system (which remains constant in absence of friction) is given by the sum of the elastic potential energy (U) and the kinetic energy (K) at any moment of the motion:

`E=U+K=(1)/(2)kx^2+(1)/(2)mv^2`

where

k is the spring constant

x is the displacement

m is the mass

v is the speed

Since E is a constant number, we immediately see from the formula that, when U increases, K decreases, and viceversa. Therefore, the maximum displacement (maximum x), which corresponds to the maximum potential energy U, will occur when K (kinetic energy) is zero. But K=0 means v=0, so when the velocity is also zero.