An 8-kg mass is attached to a spring hanging from the ceiling, thereby causing the spring to stretch 80 cm upon coming to rest at equilibrium. At time t=0, the mass is displaced 6 cm below the equilibrium position and released. At this same instant, an external force F(t) = 0.2 cos t N is applied to the system. If the damping constant for the system is 5 N-sec/m, determine the equation of motion for the mass. What is the resonance frequency for the system? C... What is the equation of motion for the mass? y(t) = (Use integers or decimals for any numbers in the expression. Round 3 to two decimal places as needed. Round all other values to five decimal places as needed.)
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.
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