# An air-track glider attached to a spring oscillates between the 12.0 cm mark and the 55.0 cm mark on the track. The glider completes 15.0 oscillationsin 37.0 s. What are the (a) period, (b)...

An air-track glider attached to a spring oscillates between the 12.0 cm mark and the 55.0 cm mark on the track. The glider completes 15.0 oscillations

in 37.0 s. What are the (a) period, (b) frequency, (c) amplitude, and (d) maximum speed of the glider?

valentin68 | Certified Educator

The equation of motion of the oscillator is

`x(t) = A*sin(omega*t+phi)`

1) The period is simply the time for one complete oscillation (or equivalent the inverse of the frequency):

`T = "time"/n =1/F = 37/15 =2.467 s`

2) The frequency, as said above is the inverse of the period:

`F = 1/T =1/2.467 =0.405 Hz`

3) The amplitude is half the difference between minimum and maximum marks on the track:

`X_max =+A` , `X_min =-A`

`A =(X_max-X_min)/2=(55-12)/2 =21.5 cm`

4)

`v(t) =dx/dt = omega*A*cos(omega*t+phi)`

`v_max =omega*A =2*pi*F*A =2*pi*0.405*0.215 =0.547 m/s`