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# Simple Pendulum Calculator

Select the term that you want to find, enter the required values, and click calculate button using simple pendulum calculator

Table of Contents:

## 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/s^{2} 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 = (T^{2} *g) / (4π^{2})

**Step 3:**

Calculation

L = (T^{2} *g) / (4π^{2})

L = (33^{2}*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 * π^{2} * L) / T^{2}

**Step 3:**

Calculation

g = (4 * (22/7)^{2} * 12) / 31^{2}

g = 0.49000 m/s^{2}