A mass m = 50 g is released from a height h = 10 cm above a vertical spring having a spring constant of 500 N m ⁻¹ , as shown in the figure. Upon impact, the mass sticks to the spring and subsequently executes simple harmonic oscillations. A concave mirror with a focal length of 12 cm is positioned facing the mass such that its principal axis aligns with the mass's line of motion. The pole of the mirror is fixed at a

Step-by-step solution

Given mass m = 50 g = 0.05 kg , height h = 10 cm = 0.1 m , and spring constant k = 500 N m ⁻¹ . The velocity of the mass just before striking the spring is v = 2gh = 2 10 0.1 = 2 m s ⁻¹ . Let the uncompressed free end of the spring be the origin. When the mass sticks to the spring, it executes simple harmonic motion (SHM). The mean position of the oscillation is at a compression x₀ where the spring force balances the gravitational force: kx₀ = mg x₀ = 0.05 10 500 = 0.001 m = 0.1 cm . The angular frequency of the SH