Question

In simple harmonic motion along the x-axis, a particle has an amplitude of xm. When its kinetic energy is 8 J, it is at:

a) x = 0
b) x = x1
c) x = xm/2
d) x = xm

Answer 1

In simple harmonic motion, a particle will have maximum kinetic energy when it is at the equilibrium position, x = 0, hence the correct answer to when its kinetic energy is 8 J is a) x = 0.

Step-by-step explanation:

In simple harmonic motion (SHM), a particle's kinetic and potential energy are constantly interchanged as it oscillates about the equilibrium position. At the position x = 0, which is the equilibrium position, the particle has maximum kinetic energy and zero potential energy. As the question states the kinetic energy is 8 J at this point, we know that the particle would be at x = 0 since that is where it has its maximum kinetic energy. Thus, the correct answer is a) x = 0. Other positions such as x = xm or x = xm/2 correspond to situations where the particle's kinetic energy would be partly converted into potential energy.