A 150 g mass is undergoing simple harmonic motion along the x-axis on an ideal spring withk=100 N/m. At t=0, the mass is at x=-10cm and is moving with velocity v=-15m/sec.a) What is the total energy of the system?b) What is the position of the mass as a function of time, x(t)?c) What is the acceleration of the mass at t=3.5sec?A system with the same mass and spring constant as question above has a damping constanty=0.9. Assume the mass was pulled to the right 30 cm at t=0 and released.d) Estimate the time at which the amplitude has decayed to 4 of its initial value.e) Assume the system is connected to a forcing function given by (in Newtons)F(t)=2coswtEstimate the value of the amplitude at resonance.

Name: A 150 g mass is undergoing simple harmonic motion along the x-axis on
Uploaded: 2024-03-20T06:58:04.000Z
Channel: Bartleby
Description: A 150 g mass is undergoing simple harmonic motion along the x-axis on an ideal spring withk=100 N/m. At t=0, the mass is at x=-10cm and is moving with velocity v=-15m/sec.a) What is the total energy of the system?b) What is the position of the mass

The given mass, m = 150 g = 0.150 kg The spring constant, k = 100 N/m At t = 0, x = -10 cm = -0.10 m…

Science

Physics

A 150 g mass is undergoing simple harmonic motion along the x-axis on an ideal spring with k=100 N/m. At t=0, the mass is at x =-10cm and is moving with velocity v= -15m/sec. a) What is the total energy of the system? b) What is the position of the mass as a function of time, x(t)? c) What is the acceleration of the mass at t=3.5sec?

A 150 g mass is undergoing simple harmonic motion along the x-axis on an ideal spring with k=100 N/m. At t=0, the mass is at x =-10cm and is moving with velocity v= -15m/sec. a) What is the total energy of the system? b) What is the position of the mass as a function of time, x(t)? c) What is the acceleration of the mass at t=3.5sec?

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 9OQ

See similar textbooks

Similar questions

A 1.50-kg mass is attached to a spring with spring constant 33.0 N/m on a frictionless, horizontal table. The springmass system is stretched to 4.00 cm beyond the equilibrium position of the spring and is released from rest at t = 0. a. What is the maximum speed of the 1.50-kg mass? b. What is the maximum acceleration of the 1.50-kg mass? c. What are the position, velocity, and acceleration of the 1.50-kg mass as functions of time?
The position of a particle attached to a vertical spring is given by y=(y0cost)j. The y axis points upward, y0 = 14.5 cm. and = 18.85 rad/s. Find the position of the particle at a. t = 0 and b. t = 9.0 s. Give your answers in centimeters.
A block of mass m = 2.00 kg is attached to a spring of force constant k = 500 N/m as shown in Figure P7.15. The block is pulled to a position xi = 5.00 cm to the right of equilibrium and released from rest. Find the speed the block has as it passes through equilibrium if (a) the horizontal surface is frictionless and (b) the coefficient of friction between block and surface is k = 0.350. Figure P7.15
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 particle with a mass of 0.500 kg is attached to a horizontal spring with a force constant of 50.0 N/m. At the moment t = 0, the particle has its maximum speed of 20.0 m/s and is moving to the left. (a) Determine the particles equation of motion, specifying its position as a function of time. (b) Where in the motion is the potential energy three times the kinetic energy? (c) Find the minimum time interval required for the particle to move from x = 0 to x = 1.0 m. (d) Find the length of a simple pendulum with the same period.
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.
Consider the data for a block of mass m = 0.250 kg given in Table P16.59. Friction is negligible. a. What is the mechanical energy of the blockspring system? b. Write expressions for the kinetic and potential energies as functions of time. c. Plot the kinetic energy, potential energy, and mechanical energy as functions of time on the same set of axes. Problems 5965 are grouped. 59. G Table P16.59 gives the position of a block connected to a horizontal spring at several times. Sketch a motion diagram for the block. Table P16.59
A spring 1.50 m long with force constant 475 N/m is hung from the ceiling of an elevator, and a block of mass 10.0 kg is attached to the bottom of the spring. (a) By how much is the spring stretched when the block is slowly lowered to its equilibrium point? (b) If the elevator subsequently accelerates upward at 2.00 m/s2, what is the position of the block, taking the equilibrium position found in part (a) as y = 0 and upwards as the positive y-direction. (c) If the elevator cable snaps during the acceleration, describe the subsequent motion of the block relative to the freely falling elevator. What is the amplitude of its motion?
A simple harmonic oscillator has amplitude A and period T. Find the minimum time required for its position to change from x = A to x = A/2 in terms of the period T.
A uniform annular ring of mass m and inner and outer radii a and b, respectively, is pivoted around an axis perpendicular to the plane of the ring at point P (Fig. P16.35). Determine its period of oscillation. FIGURE P16.35
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.