A spring stores 5 J of energy when stretched by 25 cm. It is kept vertical with the lower end fixed. A block attached to its upper end makes 5 oscillations each second. Find the mass of the block.
Physics · Simple Harmonic Motion
JEE Mains Advanced

Question

A spring stores 5 J of energy when stretched by 25 cm. It is kept vertical with the lower end fixed. A block attached to its upper end makes 5 oscillations each second. Find the mass of the block.

G1 Physics · Accepted Answer

Spring energy (1/2)kx²=5 J at x=0.25 m gives k=10/0.0625=160 N m⁻¹. Frequency is 5 Hz, so ω=10π rad s⁻¹. Hence m=k/ω²=160/(100π²)≈0.162 kg≈0.16 kg.