Describe waveform of carrier wave modulating signal and amplitude
Answers
Total Energy in Simple Harmonic Motion (T.E.)
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 a2
Hence, 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 2a2
As 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 massDirectly proportional to the square of the frequency of oscillations andDirectly proportional to the square of the amplitude of oscillation.
The law of conservation of energy states that energy can neither be created nor destroyed. Therefore, the total energy in simple harmonic motion will always be constant. However, kinetic energy and potential energy are interchangeable. Given below is the graph of kinetic and potential energy vs instantaneous displacement.