13) A type of cuckoo clock keeps time by having a mass bouncing on a spring, usu
ID: 1328501 • Letter: 1
Question
13) A type of cuckoo clock keeps time by having a mass bouncing on a spring, usually something cute like a cherub in a chair. What force constant is needed to produce a period of 0.500 s for a 0.0150 kg mass?
14) If the spring constant of a simple harmonic oscillator is doubled, by what factor will the mass of the system need to change in order for the frequency of the motion to remain the same?
22) As usual the acceleration due to gravity in these problems is taken to be 9.80 m/s squred unless otherwise specified.
What is the length of a pendulum that has a period of 0.500 s ?
26) The pendulum on a cuckoo clock is 5.00 cm long, what is its frrequency?
8) Pendulum clocks are made to run at the correct rate by adjusting the pendulum, suppose you move from one city to another where the acceleration due to gravity is slightly greater, taking your pendulum clock withyou, will you have to lengthen or shorten the pendulum to keep the correct times other factors remaining constant? Explain your answer.
( Please show all workings and solutions)
Explanation / Answer
13) The period of an oscillating mass is T = 2(m/k)
Then:
k = m (2/T)² = 0.0150 (6.28 / 0.500)² = 2.36 N/m
14)
f = (1/2)[k/m]
Since k & m appear in the same power, the mass must also be doubled to maintain the same f.
22) 6.21 cm
26)
For a simple pendulum f = 1/T = (g/L)1/2/(2) = 2.23/s
8)
For a simple pendulum the period T is proportional to (L/g)1/2. If g increases slightly, L has to increase slightly to keep the period the same. You will have to lengthen the pendulum.
For a simple pendulum f = 1/T = (g/L)1/2/(2) = 2.23/s
8)
For a simple pendulum the period T is proportional to (L/g)1/2. If g increases slightly, L has to increase slightly to keep the period the same. You will have to lengthen the pendulum.
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