At t 0 a block with mass M 5 kg moves with a velocity v 2

At t = 0 a block with mass M = 5 kg moves with a velocity v = 2 m/s at position x_o = -.33 m from the equilibrium position of the spring. The block is attached to a massless spring of SPRING CONSTANT k = 61.2 N/mand slides on a frictionless surface. At what time will the block next pass x = 0, the place where the spring is unstretched?

t₁ =

Solution

The spring and mass will oscillate with an amplitude determined by the initial amount of energy the spring was given by an external factor.

A = sqrt [x₀² + (m/k)v² ]

= sqrt [0.33² + (5/61.2) * 2² ]

= 0.66 m

x = A * sin (sqrt (k/m) * t₁)

t₁ = sin( x / A) / sqrt (k / m)

= sin (0.33 / 0.66) / sqrt ( 61.2 / 5 )

t₁ = 0.15 s