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.
1.Suppose the pendulum started losing energy at the rate 1% perperiod. As a result, the energy of the pendulum drops according toE(t)= E(t=0)*exp(-z*t). Let’s call z damping constant, it has units1/sec.
a) Find Z
b) Sketch E(t) for the time span of a few hundred periods.
c) How long will it take before the energy drops to half of theinitial value at t=0?
d) How long will it take before the max deflection angle dropsto half of the initial value at t=0?
e) If the damping was produced by a force given by F = -v*k,where v is the velocity and k is some friction coefficient, findk.
f) Suppose you are aiming to excite a resonance of this pendulumby kicking 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?
