Question

How is the time period of a simple pendulum related to the frequency of oscillations

Answer 1

time period is the time needed for one complete cycle of vibration to pass a given point .however frequency is the number of cycles the vibration complete in one second .there the relation between frequency and time period would be :- T=1/F

Answer 2

An object is undergoing simple harmonic motion (SHM) if;

the acceleration of the object is directly proportional to  its displacement from its equilibrium position.the acceleration is always directed towards the equilibrium position.

The frequency (f) of an oscillation is measure in hertz (Hz) it is the number of oscillations per second. The time for one oscillation is called the period (T) it is measured in seconds.



  

Acceleration – we can calculate the acceleration of the object at any point in it’s oscillation using the equation below.



In this equation; a = acceleration in ms-2, f = frequency in Hz, x = displacement from the central position in m.

Displacement – When using the equation below your calculator must be in radians not degrees ! we can calculate the displacement of the object at any point in it’s oscillation using the equation below.



The terms in this equation are the same as the equations above. The extra terms in this equation are: A = the amplitude (maximum displacement) in m, t = the time since the oscillation began in s.

Velocity–  we can calculate the  velocity of the object at any point in it’s oscillation using the equation below.



The terms in this equation are the same as the equations above. The extra term in this equation is: v = the velocity in ms-1.