Question

An air-track glider(m=500grams) is attached to a spring with a force constant of 79N/m. The glider is pushed 10cm to the left of zero and released from rest (@ t=0, v=0 and x=-10cm).

A)What is the postion equation as a function of time for the glider?(can you show each step, specifically for finding the phase constant)

B)What is the maximum speed of glider?

Answer 1

Given that mass, m = 0.5 kg and spring constant k = 79 N/m
Angular velocity, = SQRT[k/m]
= SQRT[79/0.5] = 12.57 rad/s

The general equation for the position of the mass, x = A cos(t + )
Where A is the maximum distance and is the phase shift
Given that at time, t = 0, x becomes - A
When t = 0,
- 10 = 10 x cos(0 + )
cos() = -1
= cos^-1(-1) =
x = A cos(t + )
= 0.1 cos(t + )

Velocity = dx/dt
= 0.1 x [ - sin(t + )]
For maximum velocity, sin(t + ) = 1
vmax = 0.1 x
= 0.1 x 12.57
= 1.257 m/s