The period of a clock pendulum T is given by the equation T = 2π √ L g where the constant L is the length of the pendulum and g is the acceleration due to gravity. The period of the clock pendulum varies slightly depending on where it is located on earth’s surface, due to small changes in g. (a) If g increases, will T increase or decrease? Does this correspond to the clock speeding up or slowing down? Explain your reasoning. (b) Find the linear approximation for T (g) centered at g = 980 cm/sec2, if the length of the pendulum is 400 cm. (c) When a clock with a 400 cm pendulum is moved from a location where g = 980 cm/sec2to a new location, its period increases by .001 sec. Estimate the amount by which g changes and approximate the value of g at the new location.
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.
The period of a clock pendulum T is given by the equation T = 2π
√
L
g where the constant L is the
length of the pendulum and g is the acceleration due to gravity. The period of the clock pendulum
varies slightly depending on where it is located on earth’s surface, due to small changes in g.
(a) If g increases, will T increase or decrease? Does this correspond to the clock speeding up or
slowing down? Explain your reasoning.
(b) Find the linear approximation for T (g) centered at g = 980 cm/sec2, if the length of the pendulum
is 400 cm.
(c) When a clock with a 400 cm pendulum is moved from a location where g = 980 cm/sec2to a
new location, its period increases by .001 sec. Estimate the amount by which g changes and
approximate the value of g at the new location.
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