Question

When an object oscillating in simple harmonic motion is at its maximum displacement from the equilibrium position. What are its of the values of its speed and the magnitude of the restoring force?( in term of maximum, minimum and zero)

Answer 1

Speed = 0

Restoring force = maximum

Step-by-step explanation:

Suppose this situation as a spring with a mass attached to it, that oscilates.

The force that the spring does (the restoring force in this case) is something like

F = K*L

where K is the constant of the spring, and L is the difference between the length of the spring (stretched) and the length of the spring at rest.

Then, when the harmonic oscillator is at its maximum displacement, L takes its maximum value, which means that at this point the restoring force must also have a maximum.

And for the velocity, at this point we have the maximum displacement, this means that, if the mass was moving to the right, after this point the mass stops going to the right, and then returns to the equilibrium position to the left.

Then the velocity has a change of sign, (like an object that reached its maximum height) this means that at that exact moment, the velocity must be zero.

Then:

Speed = 0

Restoring force = maximum