Question

A mass on the end of a spring undergoes simple harmonic motion. At the instant when the mass is at its equilibrium position, what is its instantaneous velocity? 1.Instantaneous velocity cannot be determined without additional information2.At equilibrium, its instantaneous velocity is less than its maximum but not zero.3.At equilibrium, its instantaneous velocity is at maximum4.At equilibrium, its instantaneous velocity is zero.

Answer 1

Answer:

3.At equilibrium, its instantaneous velocity is at maximum

Explanation:

The motion of a mass on the end of a spring is a simple harmonic motion. In a simple harmonic motion, the total mechanical energy of the system is constant, and it is sum of the elastic potential energy (U) and the kinetic energy of the mass (K):

$E=U+K=\frac{1}{2}kx^2+\frac{1}{2}mv^2 = const.$

where

k is the spring constant

x is the displacement of the spring from equilibrium

m is the mass

v is the speed

As we see from the formula, since the total energy E is constant, when the displacement (x) increases, the speed (v) increases, and viceversa. Therefore, when the mass is at its equilibrium position (which corresponds to x=0), the velocity of the mass will be maximum.