A mass on a spring vibrates horizontally on a smooth level surface (see the figure). Its equation of motion is x(t) = 4 cos(t), where t is in seconds and x is in centimeters. equilibrium position (a) Find the velocity and acceleration at time t. v(t) = a(t) = (b) Find the position, velocity, and acceleration of the mass at time t = 5n/6. x() - 5п %3D () =| 5л 5п In what direction is it moving at that time? 5п Since ? v 0, the particle is moving to the ---Select--- ▼

A mass on a spring vibrates horizontally on a smooth level surface (see the figure). Its equation of motion is x(t) = 4 cos(t), where t is in seconds and x is in centimeters. equilibrium position (a) Find the velocity and acceleration at time t. v(t) = a(t) = (b) Find the position, velocity, and acceleration of the mass at time t = 5n/6. x() - 5п %3D () =| 5л 5п In what direction is it moving at that time? 5п Since ? v 0, the particle is moving to the ---Select--- ▼

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 14P: In an engine, a piston oscillates with simple harmonic motion so that its position varies according...

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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.
A pendulum with a period of 2.00000 s in one location (g=9.80m/s2) is moved to a new location where the period is now 1.99796 s. What is the acceleration due to gravity at its new location?
A mass is placed on a frictionless, horizontal table. A spring (k=100N/m) , which can be stretched or compressed, is placed on the table. A 5.00-kg mass is attached to one end of the spring, the other end is anchored to the wall. The equilibrium position is marked at zero. A student moves the mass out to x=4.0 cm and releases it from rest. The mass oscillates in SHM. (a) Determine the equations of motion. (b) Find the position, velocity, and acceleration of the mass at time t=3.00 s.
A 1.00-kg glider attached to a spring with a force constant of 25.0 N/m oscillates on a frictionless, horizontal air track. At t = 0, the glider is released from rest at x = 3.00 cm (that is, the spring is compressed by 3.00 cm). Find (a) the period of the gliders motion, (b) the maximum values of its speed and acceleration, and (c) the position, velocity, and acceleration as functions of time.
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