Question

A block oscillating on a spring has an initial amplitude of 30 cm. How would you change the initial amplitude to make make the maximum kinetic energy five times greater? Express the new amplitude in (cm).

Answer 1

Spring potential energy = 1/2 k x2, where k is spring constant and x is elongation/compression

Now, if maximum kinetic energy becomes 5 times, maximum potential energy should also become 5 times.

Initially, amplitude=30 cm. So, initially, maximum potential energy=1/2 k (30)*(30) = 450 k where k is spring constant.

Also, let final amplitude be A. So, finally, maximum potential energy=1/2 k *A*A = k*A*A/2 .

Since final maximum potential energy is five times as compared to the initial maximum potential energy, k*A*A/2=5*450 k

=>A*A=2*5*450=4500

=>A=67.08 cm.

So, final amplitude is 67.08 cm.