The energy E of an oscillating body in simple harmonic motion depends on its mass M , freguency N and amplitude A . using the method of dimension analysis find the relation between E , M, N , and A

Q. The energy $E$ of an oscillating body in simple harmonic motion depends on its mass $m$, frequency $n$ and amplitude $a$. Using the method of dimensional analysis find the relation between $E,m,n$ and $a$.

Q. Consider one dimensional motion of a particle of mass $m$. It has potential energy $U=a+b{x}^2$, where $a$ and $b$ are positive constants. At origin $(x=0)$ it has initial velocity $v_0$. If performs simple harmonic oscillations. The frequency of the simple harmonic motion depends on :

Q. Obtain an expression for the kinetic energy of oscillation and potential energy of a body performing a simple harmonic motion. Show that the total energy of a particle executing simple harmonic motion is proportional to the square of the amplitude and frequency of vibration.

Q. A particle of mass 0.10 kg executes Simple harmonic motion with an amplitude 0.05 m and frequency 20 vib/s. Its energy of oscillation is

Q. Potential Energy $\left(U\right)$ of a body of unit mass moving in a one-dimension conservative force field is given by $U=(x^2-4x+3)$. All units are in S.I.
(i) Find the equilibrium position of the body.
(ii) Show that oscillations of the body about this equilibrium position is simple harmonic motion and find its time period.
(iii) Find the amplitude of oscillations if the speed of the body at equilibrium position is $2\sqrt{6}m/s$.