An object of mass M is vibrating on a horizontal frictionless table. The spring

Question

An object of mass M is vibrating on a horizontal frictionless table.  The spring constant is k, and at some instant t, the velocity is v and the displacement is x.  Which of the following statements concerning the simple harmonic motion is true? a. The potential energy stored in the spring at t is kx2. b. The kinetic energy at t is Mv2. c. The potential and kinetic energies will reach maximum values at the same time. d.  The sum of KE and PE remains constant because the motion is frictionless.

An object of mass m = 0.243 kg is vibrating on a horizontal frictionless table.  The spring has a spring constant k = 303 N/m.  It is stretched initially to xo = 0.0456 m and then released from rest.  Determine the final translational speed vf of the object when the mass reaches the un-stretched position (xf = 0).?

a. 2.12 m/s

b. 1.61 m/s

c. 1.97 m/s

d. 2.51 m/s

e. 1.75 m/s

Determine the length of a simple pendulum that will swing back and forth in simple harmonic motion with a period of 1.30 s. ?

Explanation / Answer

Apply conservation of energy

Final kinetic energy = initial elastic potential energy

(1/2)*m*v^2 = (1/2)*k*xo^2

v^2 = k*xo^2/m

v = sqrt(k*xo^2/m)

= sqrt(303*0.0456^2/0.243)

= 1.61 m/s

So, Option b is the correct answer.

use,

T = 2*pi*sqrt(L/g)

T^2 = 4*pi^2*(L/g)

==> L = g*T^2/(4*pi^2)

= 9.8*1.3^2/(4*pi^2)

= 0.420 m or 42 cm

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