30 points...
Dimension
class 11
Energy of SHM is dependent on mass and frequency and amplitude of oscillation. the relation is....
Answers
REQUIRED RELATION ➡
The total energy in simple harmonic motion is the sum of its potential energy and kinetic energy.
The total energy in simple harmonic motion is the sum of its potential energy and kinetic energy.
Thus, T.E. = K.E. + P.E. = 1/2 k ( a2 – x2) + 1/2 K x2 = 1/2 k a2Hence, T.E.= E = 1/2 m ω2a2
Equation III is the equation of total energy in a simple harmonic motion of a particle performing the simple harmonic motion.
As ω2 , a2 are constants, the total energy in the simple harmonic motion of a particle performing simple harmonic motion remains constant.
Therefore, it is independent of displacement x.As ω= 2πf , E= 1/2 m ( 2πf )2a2
∴ E= 2mπ2f 2a2As 2 and π2 constants, we have T.E. ∼ m, T.E. ∼ f 2, and T.E. ∼ a2
Thus, the total energy in the simple harmonic motion of a particle is:
●Directly proportional to its mass
●Directly proportional to the square of the frequency of oscillations and
●Directly proportional to the square of the amplitude of oscillation.
required relation .........
the total energy is simple harmonic motion