Question

Which statement describes the motion of a mass on a spring? A. It exhibits constant velocity motion. B. It exhibits simple harmonic motion. C. It exhibits circular motion. D. It exhibits only upward motion.

Answer 1

since spring force on the mass is given by

$F = -kx$

so here force is restoring in nature and it also directly depends on the displacement with respect to mean position

so here force is satisfying the condition of Simple harmonic motion

so here we can say

$a = -\frac{k}{m} x$

so here we have

$\omega^2 = \frac{k}{m}$

so here correct answer would be

B. It exhibits simple harmonic motion.

Answer 2

B. It exhibits simple harmonic motion.

m = mass attached

k = spring constant

a = acceleration of the mass

x = stretch of the spring

spring force is given as

F = - kx

the spring force causes the mass to accelerate , hence

F = ma

- kx = ma

a = - (k/m) x

since the acceleration is proportional to the displacement , hence the motion is simple harmonic in nature.