A mass m attached to free end of a spring executes SHM with a period of 1s. If the mass is increased by 3 kg the period of oscillation increases by one second, the value of mass m i s ________ kg.
Physics · Simple Harmonic Motion · time period of linear shm
JEE Mains 24 January 2023 Shift 2 Evening Shift

Question

A mass m attached to free end of a spring executes SHM with a period of 1s. If the mass is increased by 3 kg the period of oscillation increases by one second, the value of mass m i s ________ kg.

G1 Physics · Accepted Answer

For a spring-mass system, T = 2π√(m/k). Initially T = 1 s; after adding 3 kg, T' = 2 s. Therefore T/T' = √[m/(m+3)] = 1/2. Squaring gives m/(m+3) = 1/4, so 4m = m + 3 and m = 1 kg.