A body of mass m = 2,50 kg is hung on a vertical spring of spring constant k = 90 N/m. At t = 0 the body is displaced from its equilibri- um position downward by distance x0 = 13 cm and it is given an initial velocity v0 = 78 cm/s also directed downwards. a) Give the displacement x(t) of the body as a function of time. After how much time does the body pass through the equilibrium position first? b) Find the maximal displacement, speed and acceleration of the body during the motion. c) Find the total energy stored in the oscil- lation.
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 body of mass m = 2,50 kg is hung on
a vertical spring of spring constant k = 90 N/m.
At t = 0 the body is displaced from its equilibri-
um position downward by distance x0 = 13 cm
and it is given an initial velocity v0 = 78 cm/s
also directed downwards.
a) Give the displacement x(t) of the body as
a function of time. After how much time does
the body pass through the equilibrium position
first?
b) Find the maximal displacement, speed and
acceleration of the body during the motion.
c) Find the total energy stored in the oscil-
lation.
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