Question

An air-track glider attached to a spring oscillates between the 10 cm mark and the 60 cm mark on the track. The glider completes 10 oscillations in 33 s. What are the (a) period, (b) frequency, (c) amplitude, and (d) maximum speed of the glider

Answer 1

Answer:

a) Time period is 3.3 seconds

b) The frequency is 0.3030 Hz

c) amplitude is 0.25 m

d) maximum speed is 0.476 m/s

Explanation:

Given the data in the question;

a) Period

Time Period T = Time taken for one oscillation

T = 33s / 10 = 3.3 seconds

Therefore, Time period is 3.3 seconds

b) Frequency

we know that frequency is the inverse of time period

so;

Frequency f = 1/T = 1 / 3.3 s

Frequency f = 0.3030 Hz

Therefore, The frequency is 0.3030 Hz

c) amplitude

amplitude A = $\frac{1}{2}$( 60 cm - 10 cm )

A = $\frac{1}{2}$ × 50 cm

A = 25 cm

A = 0.25 m

Therefore, amplitude is 0.25 m

d) maximum speed of the glider

maximum speed $V_{max}$ = ωA

and ω = 2π/T

so maximum speed $V_{max}$ = $\frac{2\pi }{T}$A

so we substitute

so maximum speed $V_{max}$ = $\frac{2\pi }{3.3}$ × 0.25 m

so maximum speed $V_{max}$ = 0.476 m/s

Therefore, maximum speed is 0.476 m/s