We know that the equation: = -Aw?x ,describes oscillatory motion Where; k W = 2п T = and X(t) = A cos(@t + p) . %3D m Given a block with mass = 10kg the spring constant k = 500 N/m and assuming NO Friction a) What is its amplitude of oscillation? (Hint: X = A at t = 0 → X(0) = A ) b) What is v(t)? c) What is a(t)? d) What is vmax? e) What is the period? f) What is max acceleration?

We know that the equation: = -Aw?x ,describes oscillatory motion Where; k W = 2п T = and X(t) = A cos(@t + p) . %3D m Given a block with mass = 10kg the spring constant k = 500 N/m and assuming NO Friction a) What is its amplitude of oscillation? (Hint: X = A at t = 0 → X(0) = A ) b) What is v(t)? c) What is a(t)? d) What is vmax? e) What is the period? f) What is max acceleration?

College Physics

1st Edition

ISBN:9781938168000

Author:Paul Peter Urone, Roger Hinrichs

Publisher:Paul Peter Urone, Roger Hinrichs

Chapter16: Oscillatory Motion And Waves

Section: Chapter Questions

Problem 41PE: The amplitude of a lightly damped oscillator decreases by 3.0% during each cycle. What percentage of...

See similar textbooks

Similar questions

Show that the time rate of change of mechanical energy for a damped, undriven oscillator is given by dE/dt = bv2 and hence is always negative. To do so, differentiate the expression for the mechanical energy of an oscillator, E=12mv2+12kx2, and use Equation 15.51.
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 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.
An automobile with a mass of 1000 kg, including passengers, settles 1.0 cm closer to the road for every additional 100 kg of passengers. It is driven with a constant horizontal component of speed 20 km/h over a washboard road with sinusoidal bumps. The amplitude and wavelength of the sine curve are 5.0 cm and 20 cm, respectively. The distance between the front and back wheels is 2.4 m. Find the amplitude of oscillation of the automobile, assuming it moves vertically as an undamped driven harmonic oscillator. Neglect the mass of the wheels and springs and assume that the wheels are always in contact with the road.
A simple pendulum has a length of 52.0 cm and makes 82.0 complete oscillations in 2.00 min. Find (a) the period of the pendulum and (b) the value of g at the location of the pendulum.
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?
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.
In an engine, a piston oscillates with simpler harmonic motion so that its position varies according to the expression x=5.00cos(2t+6) where x is in centimeters and t is in seconds. At t = O. find (a) the position of the particle, (b) its velocity, and (c) its acceleration. Find (d) the period and (e) the amplitude of the motion.