A block of mass M is attached to two springs with spring constant K1 and K2, respectively, as shown in the figure. When the block is in the initial position, both springs are in their rest position. The block is dragged to the right a distance X, and then released. Find: 1. An expression for the horizontal acceleration of the block as a function of M, K1, K2, X. 2. An expression for the period of the oscillation of the block as a function of M, K1, K2. 3. An expression for the magnitude of the velocity of the block as it passes through the initial point again, as a function of M, K1, K2, X.
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 is attached to two springs with spring constant K1 and K2, respectively, as shown in the figure. When the block is in the initial position, both springs are in their rest position. The block is dragged to the right a distance X, and then released. Find: 1. An expression for the horizontal acceleration of the block as a function of M, K1, K2, X. 2. An expression for the period of the oscillation of the block as a function of M, K1, K2. 3. An expression for the magnitude of the velocity of the block as it passes through the initial point again, as a function of M, K1, K2, X.
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