A single degree of freedom system having mass 1 kg and stiffness

A single degree of freedom system having mass 1 kg and stiffness 10 kN/m initially at rest is subjected to an impulse force of magnitude 5 kN for 10^–4 seconds. The amplitude in mm of the resulting free vibration is

At t = 0, mass is at rest, F = 5 kN for 10^–4 seconds & amplitude = x

F = m ×	dv
	dt

F.^t₂∫^t₁ dt = m ^v₂∫^v₁dv
F(t₂ – t₁) = m × (v₂ – v₁)
5 × 10^–3 × 10_-4 = 1 × (v₂ – 0)
0.5 m/s = v₂

1	mv²₂ =	1	kx²
2		2

⇒ x = √	mv²₂	= √	1 × 0.5 × 0.5	= 5 mm
	k		10 × 1000