A mass of 1.25 kg is attached to the end of a spring whose restoring force is 160 N The mass is in a т m medium that exerts a viscous resistance of 102 N when the mass has a velocity of 4 . The viscous resistance is proportional to the speed of the object. Suppose the spring is stretched 0.08 m beyond the its natural position and released. Let positive displacements indicate a stretched spring, and suppose that external vibrations act on the mass with a force of 9 sin(4t) N at time t seconds. Find an function to express the steady-state component of the object's displacement from the spring's natural position, in m after t seconds. (Note: This spring-mass system is not "hanging", so there is no gravitational force included in the model.) u(t) = Submit Question
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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