Please show the formula and work in following questions.
1. A pendulum is timed as it swings back and forth. The clock is started when the bob is at the left end of its swing. When the bob returns to the left end for the 90th return, the clock reads 60.0s.
a) What is the period of vibration?
b) What is the frequency of vibration?
2. A particle vibrates according to the equation x=20 cos 16t, where x is in centimeters. Find its amplitude, frequency, and position at exactly t=0 s.
3. A particle oscillates according to the equation y=5.0 cos 23 t, where y is in centimeters. Find its frequency of oscillation and its position at t=0.15 s.
4. A 300-g mass at the end of an ideal spring vibrates up and down in such a way that it is 2.0 cm above the tabletop at its lowest point and 16 cm above at its highest point. Its period is 4.0 s. Determine
(a) the amplitude of vibration,
(b) the spring constant,
(c) the speed and acceleration of the mass when it is 9 cm above the table top, and
(d) the speed and acceleration of the mass when it is 12 cm above the table-top.
5. A 2.5-kg mass undergoes SHM and makes exactly 3 vibrations each second. Compute
(a) the acceleration and
(b) the restoring force acting on the body,
when its displacement from the equilibrium position is 5.0 cm.
1. Period = (Total time)/(number of cycles) = 60/90 = 0.667 (s)
Frequency = 1/Period = 1/0.667 = 1.5 (Hz)
2. x(t)=amplitude * cos wt, where w is the angular frequency = 2*Pi*frequency
Therefore, Amplitude = 20(cm), f = 16/(2*Pi) = 2.6 (Hz). When t=0, x(0)=20*cos(0)=20 (cm)
3. f = 23/(2*Pi)=3.7 (Hz). ...
Find amplitude, fruquency in different oscillation questions