7. A particle moves at a constant speed of 80 cm/s in a circle of radius 40 cm centered at the origin. (a) Find the frequency and period of the x component of its position. (b) Write an expression for the x component of its position as a function of time 1, assuming that the particle is located on the +y-axis at time t = 0. 3.1s, 0.32 Hz

7. A particle moves at a constant speed of 80 cm/s in a circle of radius 40 cm centered at the origin. (a) Find the frequency and period of the x component of its position. (b) Write an expression for the x component of its position as a function of time 1, assuming that the particle is located on the +y-axis at time t = 0. 3.1s, 0.32 Hz

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 3P: The position of a particle is given by the expression x = 4.00 cos {3.00 t + }, where x is in meters...

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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.
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.
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?