Definitions [7]
Define Speed.
The distance covered by a body in a unit time is called its speed. It is also defined as the rate of change position of a body in any direction.
Speed = distance/time
Define speed Mention its formula and unit.
Speed is the rate of change of distance.
Formula: Speed = distance /time
Unit is meter/second (m/s)
Define second’s pendulum.
A simple pendulum whose period of oscillation is exactly two seconds is called a second’s pendulum.
Define an ideal simple pendulum.
An ideal simple pendulum consists a point mass suspended from a perfectly rigid support by weightless, inextensible and perfectly flexible fibre.
An ideal simple pendulum is a heavy particle suspended by a massless, inextensible, flexible string from a rigid support.
The frequency with which a body oscillates freely is called natural frequency.
A heavy but small sized metallic bob suspended by a light, inextensible and flexible string, which performs oscillatory motion, is called a simple pendulum.
A simple pendulum whose period is two seconds is called a second's pendulum.
Formulae [7]
\[KE=\frac{1}{2}mv^2\]
\[PE=mgh\]
where,
m is mass
g is gravity
h is height
T = 2π\[\sqrt {\frac {l}{g}}\]
n = \[\frac {1}{2π}\]\[\sqrt {\frac {g}{l}}\]
T = 2π\[\sqrt{\frac {L_s}{g}}\] = 2 seconds
\[g=\frac{4\pi^2L}{T^2}\]
\[E=PE+KE\]
Key Points
- A simple pendulum is a mass on a string swinging under gravity
- Used to determine acceleration due to gravity (g)
- Energy dissipation can be analysed by plotting the square of amplitude vs. time
- At any point: total mechanical energy = PE + KE
- PE depends on height; KE depends on velocity
