What is the maximum acceleration of a platform that oscillates at amplitude 2.20 cm and frequency 6.60 Hz?
Maximum value of acceleration is 37.8 m/s2.
In a simple harmonic motion, the body undergoes acceleration for amplitude. Maximum acceleration occurs when the object is at end of its path. At those points, the force acting on the object is also maximum.
The acceleration of a body in simple harmonic motion is directly proportional to the displacement, given by
To find maximum acceleration, the angular frequency can be shown as follows:
Now using equation (i) and the given & derived values, the maximum acceleration is as follows:
Hence, the value of maximum acceleration is .
A simple harmonic oscillator consists of a block attached to a spring with k=200 N/m . The block slides on a frictionless surface, with an equilibrium point x=0 and amplitude 0.20 m. A graph of the block’s velocity v as a function of time t is shown in Fig. 15-60 . The horizontal scale is set by . What are (a) the period of the SHM, (b) the block’s mass, (c) its displacement at , (d) its acceleration at , and (e) its maximum kinetic energy.
In Figure, a block weighing 14.0 N, which can slide without friction on
an incline at angle , is connected to the top of the incline by a massless
spring of unstretched length 0.450 m and spring constant 120 N/m .
a) How far from the top of the incline is the block’s equilibrium point?
b) If the block is pulled slightly down the incline and released, what is the period
of the resulting oscillations?
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