Question

A mass is undergoing simple harmonic motion. When its displacement is 0, it is at its equilibrium position. At that moment, its speed is _______ and its acceleration is _______.0,0max,max0,maxmax,o

Answer 1

Maximum; 0

Step-by-step explanation:

As the mass moves through the equilibrium position, it is moving at its fastest speed; and there's no restoring force at that moment, so the acceleration is zero.

Answer 2

The speed is maximum and the acceleration is zero

Step-by-step explanation:

- The speed of the mass in simple harmonic motion can be found by using the law of conservation of energy. In fact, the total mechanical energy of the mass-spring system is sum of kinetic energy and elastic potential energy:

`E=K+U=(1)/(2)mv^2+(1)/(2)kx^2`

where

m is the mass

v is the speed

k is the spring constant

x is the displacement

As we can see, when the displacement is zero (x=0), the term representing the kinetic energy is maximum, so v (the speed) is also maximum.

- The acceleration of the mass in simple harmonic motion is proportional to the restoring force acting on the mass, which is given by Hook's law

`a \propto F = -kx`

where

k is the spring constant

x is the displacement

When x = 0, F = 0, so the net force acting on the mass is zero. Therefore, this also means that the acceleration of the mass is also zero: a = 0.