A pendulum has a length 1 m and a mass 1 kg. Assume Earth free fall...

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Physics

A pendulum has a length 1 m and a mass 1 kg. Assume Earth freefall acceleration equal to 10 m/s^2. When the pendulum oscillates,the maximal deflection angle is +/- 1 degree.
a) How long will it take before the energy drops to half of theinitial value at t=0?
b) How long will it take before the max deflection angle dropsto half of the initial value at t=0?
c)
If the damping was produced by a force given by F = -v*k, wherev is the velocity and k is some friction coefficient, find k.
(Hint: derive the equation of motion for the pendulum includingfriction and compare to the textbook one describing the dampedharmonic oscillations.)
d)
Suppose you are aiming to excite a resonance of this pendulum bykicking it with a periodically modulated force at a frequency f.What should be f in Hz and approximately how accurately should yoube able to adjust f, i.e. f +/- how much?
(Hint: look up the expression for the amplitude of forcedvibration of a harmonic oscillator and see how it depends on thefrequency of the external force and the dambing constant.)

Answer & Explanation Solved by verified expert

3.9 Ratings (458 Votes)

A simple pendulum is one which can be considered to be a pointmass suspended from a string or rod of negligible mass For smallamplitudes the period of such a pendulum can be approximatedbyAngular frequency can be written asFor simple pendulum the displacement from the center can bewritten asSimilarly the angular displacementwill bePotential energy PE of simplependulum isKinetic energy KE of simplependulum isTotal energy See Answer

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