The position of a 0.30 kg object attached to a spring is given by x = (0.25m)cos

Question

The position of a 0.30 kg object attached to a spring is given by x = (0.25m)cos(0.4 pi t) Determine a. the amplitude of motion b. the spring constant of the spring c. the position of the object at t = 0.30 s A 2 kg object attached to a spring is pulled 15 cm from its equilibrium position and released from rest. The period of the resulting oscillation is 2 s. Determine... a. the spring constant of the spring. b. the total energy of the system (in joules). c. the maximum speed of the object. d. the position of the object as a function of time. A swing has a length of 8 ft. Determine its period and frequency of oscillation. A guitar string of length 80 cm and mass 10 g vibrates in its 7^th harmonic mode at a frequency of 375 Hz. Sketch the standing wave pattern and determine the tension in the string.

Explanation / Answer

3.

Time period is given by:

T = 2*pi*sqrt (L/g)

Given that:

L = 8 ft = 2.4384 m

g = 9.81 m/sec^2

So,

T = 2*pi*sqrt (2.4384/9.81) = 3.13 sec

Now frequency is given by:

f = 1/T

f = 1/3.13 = 0.319 Hz

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