Simple Pendulum Calculator

Simple Pendulum Calculator

Simple pendulum calculator is used to calculate the length of the string, acceleration of gravity, and time period.

Simple pendulum

A basic pendulum is made of a heavy metallic (brass) sphere with a hook (bob) suspended from a stiff stand and clamped by a weightless, inextensible, and completely flexible thread through a slit in cork. It can oscillate in a single plane with little resistance and a modest amplitude.

For oscillations of small amplitude, the time period (T) of a simple pendulum is given by the relation,

T = 2 π √ (L/g)

Where L is the pendulum's effective length and g is the gravitational acceleration due to mass.

How to find the simple pendulum?

Example 1:

Evaluate the Time Period T when the Acceleration of Gravity(g) is 9.8 m/s² and the length of the string is 34 m.

Solution

Step 1:

Extract the given data:

g = 9.8, l = 34 m, T =?

Step 2:

Using the Time period Formula:

T = 2π √(L/g)

Step 3:

Calculation

T = 2π √ (34 / 9.8)

T = 11.700 s

Example 2:

Find the length of the string when the Acceleration of Gravity(g) is 9.8 m/s2 and the Time period is 33 s.

Solution

Step 1:

Extract the given data:

g = 9.8, T = 33 s, L =?

Step 2:

Using the length of the string Formula:

L = (T² *g) / (4π²)

Step 3:

Calculation

L = (T² *g) / (4π²)

L = (33²*9.8) / (4*(22/7)²)

L = 270.60 m

Example 3:

Evaluate the Acceleration of Gravity(g) when the length of the string is 12m and the Pendulum oscillation time 31s.

Solution

Step 1:

Extract the given data:

g =? l = 12 m, T =31

Step 2:

Using the acceleration of gravity Formula:

g = (4 * π² * L) / T²

Step 3:

Calculation

g = (4 * (22/7)² * 12) / 31²

g = 0.49000 m/s²