Question

Parts A-D are from the below information! TIA

An air-track glider attached to a spring oscillates between the 15.0 cm mark and the 61.0 cm mark on the track. The glider completes 10.0 oscillations in 31.0 s .

Part A) What is the period of the oscillations? Express your answer in seconds.

Part B) What is the frequency of the oscillations? Express your answer in hertz.

Part C) What is the amplitude of the oscillations? Express your answer in centimeters.

Part D) What is the maximum speed of the glider? Express your answer in centimeters per second.

Answer 1

(A) It is given that
10 Oscillation is taking place in 31 s , therefore
1 Oscillation will be taken place in (T)=( 31/10 ) s = 3.1 s
Therefore the time period of the oscillations would be 3.1 s.
(B) We know that
frequency = 1/T = 1/3.1 = 0.322 Hz
(C)
It is Oscillation between X = 15 cm and X = 61 cm mark
Now the range of motion will be
= 61 - 15 = 46 cm
Therefore amplitude of motion will be
A = 46/2 = 23 cm
(D)
We know that the maximum speed is given by (V_max) = wA
where w is angular frequency = 2$\pi$f = 2$\pi$*0.322 = 2.023 rad/s
V_max = 2.023*0.23 = 0.465 m/s
Hence the maximum speed would be 0.465 m/s