Convert the period in to frequency (f). Convert the frequency into angular frequ
ID: 1482706 • Letter: C
Question
Convert the period in to frequency (f). Convert the frequency into angular frequency (omega). In 1934 the Franklin Institute in Philadelphia installed a huge pendulum hanging through the building. A 81.6kg (180 pound!) steel ball hangs from a 25.9m (85 feet!) wire. The farthest the pendulum gets from the center is 0.915m. Calculate the pendulum "spring constant''. Calculate how long the pendulum takes for one oscillation. If you watched the pendulum for one minute, how many oscillations would you see? If I increase the mass on the pendulum, the period will (increase / stay the same / decrease). If I increase the length of the string, the period will (increase / stay the same / decrease), Calculate the angular frequency (omega). Set up the equations for x(t), v(t), a(t). Use the simpler forms with just A and omega. The pendulum is pushed 0.915m from equilibrium. Calculate the position and velocity t = 8.40s. Make sure your calculator is set to radians when you calculate the cosine or sine.Explanation / Answer
m = 81.6 Kg
L = 25.9 m
(a)
Spring Constant of a Simple Pendulum is given by -
k = mg/L
k = (81.6 * 9.8)/25.9
k = 30.9 N/m
Spring Constant, k = 30.9 N/m
(b)
Time period of a simple pendulum is given by -
T = 2*pi * sqrt(L/g)
T = 2*3.14 * sqrt(25.9/9.8)
T = 10.21 s
Time taken for 1 oscillation, T = 10.21 s
(c)
No of Oscillations in 1 minute = Total Time/Time taken for 1 oscillation
n = 60/10.21
n = 5.9
Approximately 6 Oscillation
(d)
T = 2*pi * sqrt(m/k)
We can clearly see, Time period is directly proportional to the mass of the pendulum.
If we Increase the mass of the Pendulum, Time period will increase.