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.)
