The time period of a mass-spring system can be calculated if the mass and the spring constant are known. The time period of a pendulum can be calculated if the length of the string is known and is independent of mass or amplitude of the swing.
Equations
Description
Equation
Time period for mass-spring system
T=2πkm
Time period for simple pendulum
T=2πgl
Constants
name
symbol
value
accelerationduetogravity
g
9.81ms−2
Variable definitions
Quantity Name
Symbol
Derived Unit
SI BASE Units
timeperiod
T
s
s
mass
m
kg
kg
springconstant
k
Nm−1
kgs−2
length
l
m
m
Mass on a spring
When a mass on a spring is pulled away from its resting position and released, the system will undergo simple harmonic motion.
The time period of the oscillations can be calculated if the masses and spring constant are known.
T=2πkm
The higher the spring constant, the smaller the time period, however the heavier the mass used, the longer the time period.
Note: The spring constant is a measure of stiffness.
Example
A 200g mass stack is attached to a spring whose spring constant is 670Nm−1. The mass stack is displaced from its resting position and released. The system undergoes simple harmonic motion. Calculate the time period of the oscillations, assume frictional forces are negligible.
Firstly, write down the known values:
m=200g=0.20kgk=670Nm−1
Next, write down the equations needed and rearrange if necessary:
T=2πkm
Then, substitute the values into the equation:
T=2π6700.20T=0.1085569...
Make sure to include units and round to the lowest number of significant figures of the values given by the question:
timeperiod,T=0.11s
The time period of the oscillation is 0.11s.
The pendulum
When a pendulum is allowed to swing, the motion can be described as simple harmonic motion.
The time period of the pendulum can be calculated if the length of the string is known.
T=2πgl
The only variable which affects the pendulum is the length of the string. It is independent of mass and amplitude of the swing, which is a common misconception.
Note: If the pendulum was swung on a different planet or the Moon, then the time period would change, due to different gravitational field strengths. However, it is for Earth.
Example
A bob is attached to a piece of string with a length of 145cm. The bob is displaced from its resting position and released. The system undergoes simple harmonic motion. Calculate the time period of the oscillations, assume frictional forces are negligible.
Firstly, write down the known values:
l=145cm=1.45m
Next, write down the equations needed and rearrange if necessary:
T=2πgl
Then, substitute the values into the equation:
T=2π9.811.45T=2.41562...
Make sure to include units and round to the lowest number of significant figures of the values given by the question:
timeperiod,T=2.42s
The time period of the oscillation is 2.42s.
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FAQs - Frequently Asked Questions
Can you calculate the time period of a mass-spring system?
The time period of a mass-spring system can be calculated if the mass and the spring constant are known.
Can you calculate the time period of a pendulum?
The time period of a pendulum can be calculated if the length of the string is known.
Does mass affect the time period of a pendulum?
The time period of a pendulum is independent of mass or amplitude of the swing.