A mass M attached to a spring, oscillates with a period of 2 s If the mass is increased by 2 kg the period increases by one s Find the initial mass M assuming that Hooke's Law is obeyed.
Physics · Simple Harmonic Motion
JEE Mains Advanced

Question

A mass M attached to a spring, oscillates with a period of 2 s If the mass is increased by 2 kg the period increases by one s Find the initial mass M assuming that Hooke's Law is obeyed.

G1 Physics · Accepted Answer

For the same spring, T∝√M. Therefore 3/2=√[(M+2)/M]. Squaring: 9/4=(M+2)/M ⇒ 9M=4M+8 ⇒ M=8/5=1.6 kg.