A simple pendulum is 8.00 m long. (a) What is the period of small oscillationsfo

Question

A simple pendulum is 8.00 m long. (a) What is the period of small oscillationsfor this pendulum if it is located in an elevator acceleratingupward at 7.00 m/s2?
1 s

(b) What is its period if the elevator is accelerating downward at7.00 m/s2?
2 s

(c) What is the period of this pendulum if it is placed in a truckthat is accelerating horizontally at 7.00 m/s2?
3 s (a) What is the period of small oscillationsfor this pendulum if it is located in an elevator acceleratingupward at 7.00 m/s2?
1 s

(b) What is its period if the elevator is accelerating downward at7.00 m/s2?
2 s

(c) What is the period of this pendulum if it is placed in a truckthat is accelerating horizontally at 7.00 m/s2?
3 s

Explanation / Answer

Given that A simple pendulum of length (L) = 8.00 m long
Acceleration due to gravity (g) =9.8m/s2 a) The period of small oscillations for this pendulum if it islocated in an elevator accelerating upward at (a)=7.00 m/s2 The reaction of the elevator on the pendulum (R) pointsupwards the weight of the pendulum points downwards When the elevator accelerated upwards, the equationbecomes                    ma =R -mg                      R =m(g+a) The net acceleration of the pendulum during upward motion is(g+a) Then the period is given by                          T = 2L/(g+a) b) When the elevator accelerated downwards, the equationbecomes                    ma =mg-R                      R =m(g-a) The net acceleration of the pendulum during downwardmotion is (g-a) Then the period is given by                          T = 2L/(g-a) c) If the pendulum is allowed to oscillate when the truck is inmotion Effective acceleration due to gravity                         geff = (9.8)+(7.0)                               = 4.098m/s2 Then we get                         T = 2L/geff now substitute all the above values to get the requiredanswer now substitute all the above values to get the requiredanswer

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