Question

An air-track glider attached to a spring oscillates between the 13.0 cm mark and the 65.0 cm mark on the track. The glider completes 14.0 oscillations in 35.0 s . What are the (a) period, (b) frequency, (c) amplitude, and (d) maximum speed of the glider?

Answer 1

Time period = 2.5 sec

Frequency = 0.4 Hz

Amplitude = 0.26 m

Maximum speed = 0.65
`(m)/(s)`

Step-by-step explanation:

No. of oscillations = 14

Time = 35 sec

(a). Time period of oscillation

`T = (35)/(14)`

T = 2.5 sec

This is the time period.

(b). Frequency

`f = (1)/(T)`

`f = (1)/(2.5)`

f = 0.4 Hz

This is the frequency.

(c). Oscillation from one side to another side is 65 - 13 = 52 cm = 0.52 m

Hence amplitude

`A = (1)/(2) (0.52)`

A = 0.26 m

This is the amplitude.

(d). The maximum speed

`v_(max) = (2 \pi f) A`

`v_(max) =` 2 × 3.14 × 0.4 × 0.26

`v_(max) =` 0.65
`(m)/(s)`