11. An 8 lb weight stretches a spring 2 inches. It is attached to a dashpot with damping constant c=4 lb-sec/ft. The weight is initially displaced 3 inches above equilibrium and given a downward velocity of 4 ft/sec. Find its displacement for t > 0. -8t 6.2.11 (p. 288) y = e¯° 4 cos 8/2t – sin 8/2t ) ft 4/2

11. An 8 lb weight stretches a spring 2 inches. It is attached to a dashpot with damping constant c=4 lb-sec/ft. The weight is initially displaced 3 inches above equilibrium and given a downward velocity of 4 ft/sec. Find its displacement for t > 0. -8t 6.2.11 (p. 288) y = e¯° 4 cos 8/2t – sin 8/2t ) ft 4/2

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 21P: A 50.0-g object connected to a spring with a force constant of 35.0 N/m oscillates with an amplitude...

See similar textbooks

Similar questions

A simple pendulum makes 120 complete oscillations in 3.00 min at a location where g = 9.80 m/s2. Find (a) the period of the pendulum and (b) its length.
The amplitude of a lightly damped oscillator decreases by 3.0% during each cycle. What percentage of the mechanical energy of the oscillator is lost in each cycle?
A block with mass m = 0.1 kg oscillates with amplitude .A = 0.1 in at the end of a spring with force constant k = 10 N/m on a frictionless, horizontal surface. Rank the periods of the following situations from greatest to smallest. If any periods are equal, show their equality in your tanking, (a) The system is as described above, (b) The system is as described in situation (a) except the amplitude is 0.2 m. (c) The situation is as described in situation (a) except the mass is 0.2 kg. (d) The situation is as described in situation (a) except the spring has force constant 20 N/m. (e) A small resistive force makes the motion underdamped.
A block-spring system oscillates with an amplitude of 3.50 cm. The spring constant is 250 N/m and the mass of the block is 0.500 kg. Determine (a) the mechanical energy of the system, (b) the maximum speed of the block, and (c) the maximum acceleration.
A 50.0-g object connected to a spring with a force constant of 35.0 N/m oscillates with an amplitude of 4.00 cm on a frictionless, horizontal surface. Find (a) the total energy of the system and (b) the speed of the object when its position is 1.00 cm. Find (c) the kinetic energy and (d) the potential energy when its position is 3.00 cm.
A simple harmonic oscillator takes 12.0 s to undergo five complete vibrations. Find (a) the period of its motion, (b) the frequency in hertz, and (c) the angular frequency in radians per second.
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.
If a simple pendulum oscillates with small amplitude and its length is doubled, what happens to the frequency of its motion? (a) It doubles. (b) It becomes 2 times as large. (c) It becomes half as large. (d) It becomes 1/2 times as large. (e) It remains the same.
Consider the damped oscillator illustrated in Figure 15.19. The mass of the object is 375 g, the spring constant is 100 N/m, and b = 0.100 N s/m. (a) Over what time interval does the amplitude drop to half its initial value? (b) What If? Over what time interval does the mechanical energy drop to half its initial value? (c) Show that, in general, the fractional rate at which the amplitude decreases in a damped harmonic oscillator is one-half the fractional rate at which the mechanical energy decreases.
Damping is negligible for a 0.150-kg object hanging from a light, 6.30-N/m spring. A sinusoidal force with an amplitude of 1.70 N drives the system. At what frequency will the force make the object vibrate with an amplitude of 0.440 m?
Is it possible to have damped oscillations when a system is at resonance? Explain.