Answer:
A) 2.75 m/s B) 0.1911 m C) 0.109 s
Explanation:
mass of block = M =0.1 kg
spring constant = k = 21 N/m
amplitude = A = 0.19 m
mass of bullet = m = 1.45 g = 0.00145 kg
velocity of bullet = vᵇ = 68 m/s
as we know:
Angular frequency of S.H.M = ω₀ = 
= 
= 14.49 rad/sec
<h3>A) Speed of the block immediately before the collision:</h3>
displacement of Simple Harmonic Motion is given as:

Differentiating this to find speed of the block immediately before the collision:

As bullet strikes at equilibrium position so,
φ = 0
t= 2nπ
⇒ cos (ω₀t + φ) = 1
⇒ 

<h3>B) If the simple harmonic motion after the collision is described by x = B sin(ωt + φ), new amplitude B:</h3>
S.H.M after collision is given as :

To find B, consider law of conservation of energy

<h3>C) Time taken by the block to reach maximum amplitude after the collision:</h3>
Time period S.H.M is given as:

Collision occurred at equilibrium position so time taken by block to reach maximum amplitude is equal to one fourth of total time period
