Derive the expression for total energy of a particle executing simple harmonic motion (SHM).

Give the expression for the potential energy of a particle executing SHM.

Give the expression for centripetal force on the particle executing uniform circular motion.

The potential energy function for a particle executing linear simple harmonic motion is given by V(x)= kx^(2)"/"2 , where k is the force constant of the oscillator. For k= 0.5 Nm^(1) , the graph of V(x) versus x is shown in Fig. 6. 12. Show that a particle of total energy 1 J moving under this potential must 'turn back' when it reaches x= pm 2m .

Obtain the expression for total energy of a circularly orbiting satellite.

Derive the expression for energy stored in a charged capacitor.