An object of mass 0.2 kg executes SHM along the x-axis with frequency of (25/π) Hz. At the point x = 0.04m the object has KE 0.5 J and PE 0.4 J. The amplitude of oscillation is .
Physics · Simple Harmonic Motion
JEE Mains Advanced

Question

An object of mass 0.2 kg executes SHM along the x-axis with frequency of (25/π) Hz. At the point x = 0.04m the object has KE 0.5 J and PE 0.4 J. The amplitude of oscillation is .

G1 Physics · Accepted Answer

f=25/π Hz ⇒ ω=2πf=50 rad s⁻¹. With m=0.2 kg, k=mω²=500 N m⁻¹. At x=0.04 m, total energy E=K+U=0.9 J. Since E=(1/2)kA², A=√(2E/k)=√(1.8/500)=0.06 m.