A mass (m = 10 kg) is attached to a spring and with simple harmonic motion along

Question

A mass (m = 10 kg) is attached to a spring and with simple harmonic motion along an x-axis. Its displacement from the origin varies with time according to the equation: x(t) = (6.00m) cos(pi/4 t) Determine the amplitude; angular frequency; frequency; and period of the motion. Find the velocity function of the mass at any time t. Find the acceleration function of the mass at any time t. Using the results in part (b) and (c), determine at time t = 1.00 s; the position; the velocity; and the acceleration, Determine for the mass the following; the maximum displacement; the maximum speed; and the maximum acceleration. Sketch a graph of v(t) for 1 1/2 wavelengths.

Explanation / Answer

2)

x = 6 * cos(pi/4 * t)

as x = A * cos(w * t)

where A is amplitude

w is the angular frequency

i) comparing both the equations

A = 6 m

the amplitude is 6 m

ii)

angular frequency = w

angular frequency = pi/4 rad/s

angular frequency = 1.571 rad/s

iii)

frequency = w/2pi

frequency = (pi/4)/(2pi)

frequency = 1/8 Hz

the frequency is 0.125 Hz

iv)

period of motion = 1/f

period of motion = 1/(1/8)

period of motion = 8 s

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