Answer:
D) The objects velocity is zero when its acceleration is a maximum
Explanation:
In a simple harmonic motion, the total energy is constant (if we neglect air resistance and friction), and it is equal to the sum of the elastic potential energy U and the kinetic energy K:
[tex]E=K+U=\frac{1}{2}mv^2+\frac{1}{2}kx^2[/tex] (1)
where
m is the mass
v is the velocity
k is the spring constant
x is the displacement
As a consequence, since E must remain constant, when K increases U decreases, and vice-versa.
Also, in a simple harmonic motion the acceleration of the system is proportional to the negative of the displacement:
[tex]a\propto - x[/tex] (2)
So, combining (1) with (2), we have the following situations:
- When the displacement is zero (x=0), the acceleration is also zero (a=0), and so the velocity is maximum, because the kinetic energy is maximum
- When the displacement is maximum (x=max), the acceleration is also maximum, while the velocity is zero because the kinetic energy is zero
So, the correct statement is
D) The objects velocity is zero when its acceleration is a maximum
