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):
[tex]E=U+K=\frac{1}{2}kx^2+\frac{1}{2}mv^2[/tex] (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):
[tex]a\propto - x[/tex]
So, this means that at the point of maximum displacement, the acceleration is maximum and the velocity is zero.
