35. A simple pendulum has a length of 52.0 cm and makes 82.0 complete oscillations in 2.00 min. Find (a) the period of the pendulum and (b) the value of g at the location of the pendulum.
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.
Answer 35 only. Explain and show complete solution with given. Label the formulas used.
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of 320 kg sit
13.5 Motion of a Pendulum
their weight
cm. (a) What
34. W A man enters a tall tower, needing to know its
ags? (b) The
ce it up and
bration?
height. He notes that a long pendulum extends from
the ceiling almost to the floor and that its period is
15.5 s. (a) How tall is the tower? (b) If this pendulum
is taken to the Moon, where the free-fall acceleration is
1.67 m/s, what is the period there?
ionless hori-
ng constant
and the left
35. A simple pendulum has a length of 52.0 cm and makes
82.0 complete oscillations in 2.00 min. Find (a) the
period of the pendulum and (b) the value of g at the
location of the pendulum.
4.5 cm from
iod at which
(c) its speed
um position.
36. A "seconds" pendulum is one that moves through its
equilibrium position once each second. (The period
of the pendulum is 2.000 s.) The length of a seconds
pendulum is 0.992 7 m at Tokyo and 0.994 2 m at Cam-
bridge, England. What is the ratio of the free-fall accel-
erations at these two locations?
to a spring
ression x =
E this motion,
ne amplitude
t 3D 0 that the
37. A pendulum clock that works perfectly on the Earth is
taken to the Moon. (a) Does it run fast or slow there?"
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