A block attached to the end of a spring moves in simple harmonic motion according to the position function x(t) = X*cos*[(2*pi*t)/T) where the period of the motion is 4.0s and the amplitude of the motion is 15 cm. a) Determine the first time at which the acceleration of the block is 29.4cm/s2 b) Determine the maximum speed of the block. c) Suppose that the mass of the block is 1 kg. Determine the stiffness constant of the spring. d) Determine the magnitude of the maximum acceleration of the block.
Simple harmonic motion
Simple harmonic motion is a type of periodic motion in which an object undergoes oscillatory motion. The restoring force exerted by the object exhibiting SHM is proportional to the displacement from the equilibrium position. The force is directed towards the mean position. We see many examples of SHM around us, common ones are the motion of a pendulum, spring and vibration of strings in musical instruments, and so on.
Simple Pendulum
A simple pendulum comprises a heavy mass (called bob) attached to one end of the weightless and flexible string.
Oscillation
In Physics, oscillation means a repetitive motion that happens in a variation with respect to time. There is usually a central value, where the object would be at rest. Additionally, there are two or more positions between which the repetitive motion takes place. In mathematics, oscillations can also be described as vibrations. The most common examples of oscillation that is seen in daily lives include the alternating current (AC) or the motion of a moving pendulum.
A block attached to the end of a spring moves in
where the period of the motion is 4.0s and the amplitude of the motion is 15 cm.
a) Determine the first time at which the acceleration of the block is 29.4cm/s2
b) Determine the maximum speed of the block.
c) Suppose that the mass of the block is 1 kg. Determine the stiffness constant of the spring.
d) Determine the magnitude of the maximum acceleration of the block.
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