Question

What is the relation between time (T) and frequency (f) of an oscillation of a simple pendulum?
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Answer 1

Answer:

Time period it is defined as the time taken by the particle executing SHM.

T= 2π √(l/g )

T= 1/ν

ν = 1/2Π√(g/l )

T= 2 π /ω

Answer 2

Explanation:

When you pluck a guitar string, the resulting sound has a steady tone and lasts a long time. Each successive vibration of the string takes the same time as the previous one. We define periodic motion to be a motion that repeats itself at regular time intervals, such as exhibited by the guitar string or by an object on a spring moving up and down. The time to complete one oscillation remains constant and is called the period T. Its units are usually seconds, but may be any convenient unit of time. The word period refers to the time for some event whether repetitive or not; but we shall be primarily interested in periodic motion, which is by definition repetitive. A concept closely related to period is the frequency of an event. For example, if you get a paycheck twice a month, the frequency of payment is two per month and the period between checks is half a month. Frequency f is defined to be the number of events per unit time. For periodic motion, frequency is the number of oscillations per unit time. The relationship between frequency and period is

$f = \frac{1}{t}$

The SI unit for frequency is the cycle per second, which is defined to be a hertz (Hz):

$1hz = 1 \frac{cycle}{sec} \: or \: 1hz = \frac{1}{s}$

A cycle is one complete oscillation. Note that a vibration can be a single or multiple event, whereas oscillations are usually repetitive for a significant number of cycles.