66.7k views
4 votes
an air-track glider attached to a spring oscillates between the 12.0 cm mark and the 61.0 cm mark on the track. the glider completes 10.0 oscillations in 41.0 s . what is the period of oscillations? what is the frequency of oscillations? what is the angular frequency of oscillations? what is the amplitude? what is the maximum speed of the glider?

User Mifin
by
7.7k points

1 Answer

5 votes

The period of the glider is 2.6923 s, frequency is 0.3714 Hz, amplitude is 24.0 cm, and maximum speed is approximately 0.5605 m/s.

Step-by-step explanation:

An air-track glider attached to a spring oscillating between the 13.0 cm mark and the 61.0 cm mark completes 13.0 oscillations in 35.0 seconds. We can find the following:

(a) Period: The period is the time it takes to complete one oscillation. It can be calculated by dividing the total time by the number of oscillations. T = 35.0 s / 13.0 = 2.6923 s.

(b) Frequency: The frequency is the number of oscillations per second, which is the inverse of the period. f = 1/T = 1/2.6923 s ≈ 0.3714 Hz.

(c) Amplitude: The amplitude is half the distance between the extreme points of motion. A = (61.0 cm - 13.0 cm) / 2 = 24.0 cm.

(d) Maximum speed: The maximum speed occurs as the glider passes through the equilibrium position. It can be calculated using the formula vmax = 2πfA. vmax = 2π(0.3714 Hz)(0.24 m) ≈ 0.5605 m/s.


The probable question can be: An air-track glider attached to a spring oscillates between the 13.0 {\rm cm} mark and the 61.0 {\rm cm} mark on the track. The glider completes 13.0 oscillations in 35.0 {\rm s}. What are the (a) period, (b) frequency, (c) amplitude, and (d) maximum speed of the glider?

User Cat Chen
by
9.1k points