amplitude of oscillation

Question

a block of mass m is attached to an ideal spring with spring constant k. The block is at rest at the equilibrium position when a force is quickly applied to the block that gives it an initial speed v. What is the amplitude of the resulting oscillations

Answer 1

x(t) = A sin(ωt + φ)

 

x(0) = 0 ⇒ A sin(φ) = 0 ⇒ φ = 0

 

x(t) = A sin(ωt)

 

v(0) = dx/dt |_t=0 = v  

 

ωA cos(ωt) |_t=0 = v ⇒

 

ωA = v

 

A = v/ω = v/√(k/m) = v√(m/k)

 

A = v √(m/k)