Simple Harmonic Motion of Pendulums Video Lessons

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Problem: The shadow of a pendulum cast on a 7t board moves on a straight line. By placing the x-axis on the straight line with the origin at the middle of the total path, the x-coordinate of the shadow is given by the following function: x(t) = 52cos(πt), where t is in seconds and x is in centimetersPart (a) Find the speed, in centimeters per second, of the shadow at t = ¼ sPart (b) Find the speed, in centimeters per second, of the shadow at t = ½ sPart (c) Find the magnitude of the acceleration, in meters per second squared, of the shadow’s motion at t = 1/3 sPart (d) How much distance, in centimeters, does the shadow travel in 20 sec?

FREE Expert Solution

Velocity is expressed as:

v=dxdt

Acceleration:

a=dvdt

Part (a)

From our velocity equation:

v=ddt[52cos(πt)]=-52πsin(πt)

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Problem Details

The shadow of a pendulum cast on a 7t board moves on a straight line. By placing the x-axis on the straight line with the origin at the middle of the total path, the x-coordinate of the shadow is given by the following function: x(t) = 52cos(πt), where t is in seconds and x is in centimeters

Part (a) Find the speed, in centimeters per second, of the shadow at t = ¼ s

Part (b) Find the speed, in centimeters per second, of the shadow at t = ½ s

Part (c) Find the magnitude of the acceleration, in meters per second squared, of the shadow’s motion at t = 1/3 s

Part (d) How much distance, in centimeters, does the shadow travel in 20 sec?

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