Question

A block of mass m attached to a horizontally mounted spring with spring constant k undergoes simple harmonic motion on a rictionless surface. How would the maximum speed of the block be affected i the spring constant was increased by a factor of 4 while holding the amplitude of oscillation constant?

1) It would remain unchanged.
2) It would increase by a factor of 2.
3) It would decrease by a factor of 1/4
4) It would increase by a factor of 4.
5) It would decrease by a factor of 1/2

Answer 1

To solve this problem it is necessary to apply the concepts related to simple harmonic movement.

The maximum speed from the simple harmonic motion is given as

`V = A\sqrt{(K)/(m)}`

Where,

K = Spring constant

m = mass

At this case m is a constant then

`V \propto √(K)`

then the ratio is given by

`(v_2)/(v_1)=\sqrt{(K_1)/(K_2)}`

According the statement,

`v_2 = \sqrt{(K_1)/(K_2)}v_1`

`v_2 = 2v_1`

Therefore the maximum speed becomes double: 2) It would increase by a factor of 2.