A system consists of a vertical spring with force constant k = 1 250 N/m, length L = 1.50 m, and object of mass m = 5.00 kg attached to the end (Fig. P13.76). The object is placed at the level of the point of attachment with the spring unstretched, at position yi = L, and then it is released so that it swings like a pendulum. (a) Write Newton’s second law symbolically for the system as the object passes through its lowest point. (Note that at the lowest point, r = L − yf.) (b) Write the conservation of energy equation symbolically, equating the total mechanical energies at the initial point and lowest point. (c) Find the coordinate position of the lowest point. (d) Will this pendulum’s period be greater or less than the period of a simple pendulum with the same mass m and length L? Explain.
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 system consists of a vertical spring with force constant k = 1 250 N/m, length L = 1.50 m, and object of mass m = 5.00 kg attached to the end (Fig. P13.76). The object is placed at the level of the point of attachment with the spring unstretched, at position yi = L, and then it is released so that it swings like a pendulum. (a) Write Newton’s second law symbolically for the system as the object passes through its lowest point. (Note that at the lowest point, r = L − yf.) (b) Write the conservation of energy equation symbolically, equating the total mechanical energies at the initial point and lowest point. (c) Find the coordinate position of the lowest point. (d) Will this pendulum’s period be greater or less than the period of a simple pendulum with the same mass m and length L? Explain.
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