The equation of motion of a particle undergoing simple harmonic motion is x=4.00sin0.500t, where x is in centimeters. At t=1.00 s, determine the particle's displacement, velocity, and acceleration.
SOLUTION :
Given :
x = 4.00 sin (0.500 t)
So,
Displacement x, at t = 1.00 s is :
= 4.00 sin (0.500 * 1.00)
= 1.92 cm (ANSWER).
Velocity v(t) = d/dt(4.00 sin (0.500 t)) = 4.00 * 0.500 cos(0.500 t)
=> v(1.00) = 2.00 cos(0.500 * 1.00)
=> v(1.00) = 1.7555 cm/s (ANSWER).
Acceleration a(t) = d/dt(2.00 cos (0.500 t)) = - 2.00 * 0.500 sin (0.500 t)
=> a(1.00) = - 1.00 sin (0.500 * 1.00)
=> a(1.00) = - 0.48 cm/s^2 (ANSWER).
The equation of motion of a particle undergoing simple harmonic motion is x=4.00sin0.500t, where x is...
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