Question: The angle of the pendulum in Figure is given by . If at t = 0 , and ,
(Hint: Don’t confuse the rate at which changes with the of the SHM.)
The oscillations of the simple pendulum can be defined by the equation of simple harmonic motion. The simple harmonic motion is the motion in which the acceleration of the oscillating object is directly proportional to the displacement. The force caused by the acceleration is called restoring force. This restoring force is always directed towards the mean position.
Compare the given equation with the equation of displacement of the particle in simple harmonic motion.
The phase constant :
The expression for the displacement of the particle in simple harmonic motion is
Here, x (t) is the displacement, xm is amplitude, angular velocity, t is time, is phase difference.
For angular displacement, replace x by , then
The expression for velocity of the particle in simple harmonic motion is
For angular motion, replace x by , then
Divide equation (ii) by equation (i)
Therefore, the phase constant is 0.845 rad .
For t =0, equation (i) becomes as
The maximum angle is 0.0602 rad
A block of mass, at rest on a horizontal frictionless table, is attached to a rigid support by a spring of constant. A bullet of massand velocityof magnitudstrikes and is embedded in the block (SeeFigure). Assuming the compression of the spring is negligible until the bullet is embedded.
(a) Determine the speed of the block immediately after the collision and
(b) Determine the amplitude of the resulting simple harmonic motion.
Question: In Figure, the pendulum consists of a uniform disk with radius r = 10.cm and mass 500 gm attached to a uniform rod with length L =500mm and mass 270gm.
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