An oscillator consisting of a block of mass attached to a spring of force constant…

PHYSICS · Multi-part · A Level · Physics · Further mechanics and thermal physics · Further mechanics and thermal physics

Problem

An oscillator consisting of a block of mass

m

attached to a spring of force constant

k

has amplitude

A

and total mechanical energy

E_{0}

. The system is modified such that the amplitude becomes

pA

and the spring is replaced by another of force constant

qk

, while the mass remains the same. (a) Derive an expression for the new total mechanical energy

E

in terms of

E_{0}

p

and

q

. (b) Using the result of part (a), determine the values of

p

and

q

required for the total mechanical energy to become nine times the original value while the amplitude becomes three times the original value.