Define the effective potential energy

Reference no: EM13501061

one block of mass m slides without friction on horizontal table. The block is attached to one end of a massless spring of equilibrium length L0 and spring constant k. The other end of the spring is attached to a point on the table, such that the spring can rotate around this point without friction.

(a) What is the net force acting on the block?

(b) Find the expression for the kinetic energy T, the potential energy U, and the magnitude of the angular momentum l of the particle in polar coordinates. Then express T in terms of l.

(d) Find the angular velocity of the rotational motion of the block ?R such that the block moves exactly on a circular orbit of radius R.

(e) Show that if ? is close to ?R, the block will oscillate around the orbit of radius R and the motion in the radial coordinate will be that of a simple harmonic oscillator. Find the frequency of such small oscillations.

Reference no: EM13501061

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