A mass on a spring vibrates horizontally on a smooth level surface (see the figure). Its equation of motion is x(t) = 10 cos(t), where t is in seconds and x is LE equilibrium position Exercise (a) Find the velocity and acceleration at time t. Step 1 If the equation of motion is given by f(t), then the velocity is given by F '(t) f'(t) and the acceleration is given by f"(t) f "(t) Step 2 Therefore, for x(t) = 10 cos(t), the velocity at time t is given by v(t) = x'(t) =-10 sin (1) – 10 sin (t) and the acceleration at time t is given by a(t) = x"(t) = | –10 cos (t) |-10 cos (t) Exercise (b) Find the position, velocity, and acceleration of the mass at time t = 1/6. In what direction is it moving at that time?

A mass on a spring vibrates horizontally on a smooth level surface (see the figure). Its equation of motion is x(t) = 10 cos(t), where t is in seconds and x is LE equilibrium position Exercise (a) Find the velocity and acceleration at time t. Step 1 If the equation of motion is given by f(t), then the velocity is given by F '(t) f'(t) and the acceleration is given by f"(t) f "(t) Step 2 Therefore, for x(t) = 10 cos(t), the velocity at time t is given by v(t) = x'(t) =-10 sin (1) – 10 sin (t) and the acceleration at time t is given by a(t) = x"(t) = | –10 cos (t) |-10 cos (t) Exercise (b) Find the position, velocity, and acceleration of the mass at time t = 1/6. In what direction is it moving at that time?

University Physics Volume 1

18th Edition

ISBN:9781938168277

Author:William Moebs, Samuel J. Ling, Jeff Sanny

Publisher:William Moebs, Samuel J. Ling, Jeff Sanny

Chapter15: Oscillations

Section: Chapter Questions

Problem 14CQ: With the use of a phase shift, the position of an object may be modeled as a cosine or sine...

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