A mass m attached to a spring is subjected to a harmonic

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A mass m attached to a spring is subjected to a harmonic force as shown in figure. The amplitude of the forced motion is observed to be 50 mm. The value of m (in kg) is

1. 0.1
2. 1.0
3. 0.3
4. 0.5

Correct Option: A

Given: Amplitude of force motion, A = 50 mm
∴ F(t) = 100 cos (100t) ...(i)

ω = 100
General solution is, x = A cos ωt

Putting in equation (i), we have
m (- Aω² cosωt) + K (A cosωt) = 100 cos (ωt)
⇒ – mω²A + kA = 100
Here k = 3000 N/m
∴ – m (0.05) (100)² + 3000 (0.05) = 100

m =	50	= 0.1
	100