If the spring constant is doubled, what value does the period have for a mass on a spring? a. the period would double by square `sqrt(2)`. b. the period would be halved by `sqrt(2)`. c. the period would increase by `sqrt(2)`. d. the period would decrease by `sqrt(2)`.

The period would decrease by sqrt(2)

Explanation:

The restoring force is given by,

F = -kx

According to Newton's second law of motion,

ma = -kx

ma + kx = 0

The time period is given by,

T =

Where is the angular velocity and it is given by,

=

Now if the spring constant is doubled then,

Thus,

=

Thus, The period would decrease by sqrt(2).

Hence, option D is correct.

an energy transformation flow diagram is shown

where is it ?