An object of mass 0.2 kg executes simple harmonic motion along x axis with frequency of $\left(\frac{25}{\pi}\right)$ Hz. At the position $x=0.04$ m the object has kinetic energy 0.5 J and potential energy 0.4 J. The amplitude of oscillation is _____ cm.

JEE Main · 2024 · 08 Apr 2024 · Shift 2 · Elasticity & SHM

An object of mass 0.2 kg executes simple harmonic motion along x axis with frequency of

(\frac{25}{π})

Hz. At the position

x = 0.04

m the object has kinetic energy 0.5 J and potential energy 0.4 J. The amplitude of oscillation is _____ cm.

Answer: 6

Total mechanical energy at

x = 0.04

E = K E + P E = 0.5 + 0.4 = 0.9

E = \frac{1}{2} m ω^{2} A^{2}, ω = 2 π f = 2 π (\frac{25}{π}) = 50 rad/s

0.9 = \frac{1}{2} (0.2) (50)^{2} A^{2} = 250 A^{2} ⟹ A^{2} = 0.0036 ⟹ A = 0.06 m = 6 cm

JEE Main · 2024 · 08 Apr 2024 · Shift 2 · Integer answer