A block of mass m = 0.786 kg is fastened to an unstrained horizontal spring whose spring constant is k = 99.3 N/m. The block is given a displacement of +0.169 m, where the + sign indicates that the displacement is along the +x axis, and then released from rest. (a) What is the force (with sign) that the spring exerts on the block just before the block is released? (b) What is the amplitude? (c) Find the angular frequency of the resulting oscillatory motion. (d) What is the speed of the block at the equilibrium point? (e) Determine the magnitude of the acceleration of the block at the equilibrium point.
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 of mass m = 0.786 kg is fastened to an unstrained horizontal spring whose spring constant is k = 99.3 N/m. The block is given a displacement of +0.169 m, where the + sign indicates that the displacement is along the +x axis, and then released from rest. (a) What is the force (with sign) that the spring exerts on the block just before the block is released? (b) What is the amplitude? (c) Find the angular frequency of the resulting oscillatory motion. (d) What is the speed of the block at the equilibrium point? (e) Determine the magnitude of the acceleration of the block at the equilibrium point. (f) How long does it take the block to return to its original displacement?
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