5. A "seconds pendulum" is one that moves throughits equilibrium position once each second. (Theperiod of the pendulum is precisely 2 s.) The lengthof a seconds pendulum is 0.992 7 m at Tokyo, Japanand 0.994 2 m at Cambridge, England. What is theratio of the free-fall accelerations at these twolocations?

The given values with suitable variables are listed below. Here, LT denotes the seconds’ pendulum…

Answered: 5. A "seconds pendulum" is one that…

Principles of Physics: A Calculus-Based Text

5th Edition

ISBN:9781133104261

Author:Raymond A. Serway, John W. Jewett

Publisher:Raymond A. Serway, John W. Jewett

Chapter12: Oscillatory Motion

Section: Chapter Questions

Problem 26P

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(a) What is the effect on the period of a pendulum if you double its length? (b) What is the effect on the period of a pendulum if you decrease its length by 5.00%?
A clock is constructed so that it keeps perfect time when its simple pendulum has a period of 1.000 s at locations where g = 9.800 m/s2. The pendulum bob has length L = 0.248 2 m, and instead of keeping perfect time, the clock runs slow by 1.500 minutes per day. (a) What is the free-fall acceleration at the clocks location? (b) What length of pendulum bob is required for the clock to keep perfect time?
A simple pendulum has mass 1.20 kg and length 0.700 m. (a) What is the period of the pendulum near the surface of Earth? (b) If the same mass is attached to a spring, what spring constant would result in the period of motion found in part (a)?
A spring of negligible mass stretches 3.00 cm from its relaxed length when a force of 7.50 N is applied. A 0.500-kg particle rests on a frictionless horizontal surface and is attached to the free end of the spring. The particle is displaced from the origin to x = 5.00 cm and released from rest at t = 0. (a) What is the force constant of the spring? (b) What are the angular frequency , the frequency, and the period of the motion? (c) What is the total energy of the system? (d) What is the amplitude of the motion? (c) What are the maximum velocity and the maximum acceleration of the particle? (f) Determine the displacement x of the particle from the equilibrium position at t = 0.500 s. (g) Determine the velocity and acceleration of the particle when t = 0.500 s.
At what rate will a pendulum clock run on the Moon, where the acceleration due to gravity is 1.63 m/s2, if it keeps time accurately on Earth? That is, find the time (in hours) it takes the clock’s hour hand to make one revolution on the Moon.
Review. A dock with a brass pendulum has a period of 1.000 s at 20.0C. If the temperature increases to 30.0C, (a) by how much does the period change and (b) how much time does the clock gain or lose in one week?
A clock is constructed so that it keeps perfect time when its simple pendulum has a period of 1.000 s at locations where g = 9.800 m/s2. The pendulum bob has length L = 0.248 2 m, and instead of keeping perfect time, the clock runs slow by 1.500 minutes per day. (a) What is the free-fall acceleration at the clocks location? (b) What length of pendulum bob is required for the clock to keep perfect time?
At what rate will a pendulum clock run on me Moon, where the acceleration due to gravity is 1.63 m/s2, if it keeps time accurately on Earth? That is, find the time (in hours) it takes me clock's hum hand to make one revolution on the Moon.
We do not need the analogy in Equation 16.30 to write expressions for the translational displacement of a pendulum bob along the circular arc s(t), translational speed v(t), and translational acceleration a(t). Show that they are given by s(t) = smax cos (smpt + ) v(t) = vmax sin (smpt + ) a(t) = amax cos(smpt + ) respectively, where smax = max with being the length of the pendulum, vmax = smax smp, and amax = smax smp2.
If a pendulum-driven clock gains 5.00 s/day, what fractional change in pendulum length must be made for it to keep perfect time?
Is it possible to have damped oscillations when a system is at resonance? Explain.
. A mass of 0.75 kg is attached to a relaxed spring with k = 2.5 N/m. The mass rests on a horizontal, frictionless surface. If the mass is displaced by 0.33 m, what is the magnitude of the force exerted on the mass by spring? If the mass is then released to execute simple harmonic along the surface, with what frequency will it oscillate?

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