"A block oscillating on a spring has an..." was answered by students like you

Alfred Martin

Answered question

2022-01-04

A block oscillating on a spring has an amplitude of 20 cm. What will the amplitude be if the total energy is doubled? And explain.

Mary Goodson

Beginner2022-01-05Added 37 answers

In the simple harmonic motion, the energy is conserved and the total mechanical energy

E

has an exprwssion in terms of the force constant

k

and amplitude

A

as we have in the equation:

E = K + U

\frac{1}{2} k A^{2} = \frac{1}{2} m v^{2} + \frac{1}{2} k x^{2}

The total mechanical energy:

E = \frac{1}{2} k A^{2}

A = \sqrt{\frac{2 E}{k}}

As we have in the equation 1, the amplitude is directly propotional to square root of

E

A = \sqrt{E}

k

is constant, we can find the amplitude for two instants when

E

is doubled by

\frac{A_{1}}{A_{2}} = \frac{\sqrt{E}}{\sqrt{2 E}}

\frac{A_{1}}{A_{2}} = \frac{1}{\sqrt{2}}

A_{2} = \sqrt{2} A_{1}

A_{2} = \sqrt{2} (20 c m)

A_{2} = 28.28 c m

Do you have a similar question?

Recalculate according to your conditions!

Didn't find what you were looking for?