Question

Which one of the following statements is true concerning an object executing simple harmonic motion?A) The objects velocity is never zeroB) The objects acceleration in never zeroC) The objects velocity and acceleration are simultaneously zeroD) The objects velocity is zero when its acceleration is a maximumE) The objects maximum acceleration is equal to its maximum velocity

Answer 1

Answer:

D) The objects velocity is zero when its acceleration is a maximum

Explanation:

In a simple harmonic motion, the total energy is the sum of elastic potential energy (U) and kinetic energy (K):

$E=U+K=\frac{1}{2}kx^2+\frac{1}{2}mv^2$ (1)

where

k is the spring constant

x is the displacement

m is the mass

v is the velocity

The total energy E remains constant during the motion, so from the equation (1), we see that:

- At the equilibrium position, the displacement (x) is zero, so the velocity (v) is maximum

- At the point of maximum displacement, the displacement (x) is maximum, while the velocity (v) is zero

Let's also keep in mind that in a simple harmonic motion, the acceleration is directly proportional to the displacement (just the direction is opposite):

$a\propto - x$

So, this means that at the point of maximum displacement, the acceleration is maximum and the velocity is zero.