A horizontal spring with a spring constant of 75 N/m has one end attached to a w

Question

A horizontal spring with a spring constant of 75 N/m has one end attached to a wall and the other end attached to a block with a mass of 2.0 kg. The block is on a horizontal, frictionless surface. Let x = 0 be the position of the Nock when the spring is at its equilibrium length. The block is pulled to the side and released, so that it oscillates at the end of the spring in simple harmonic motion. The maximum speed of the block is 0.45 m/s. (a) What arc the angular frequency, frequency, and period of the block? (b) What is the amplitude of the blocks motion? (c) What is the equation for the simple harmonic motion of the block? Put all quantities in $1 units.

Explanation / Answer

Given Data

Spring Constant , k = 75 N/m

Mass of block , m = 2 kg

max. speed, vmax = 0.45 m/s

Solution :-

a)

For a body in SHM angular frequency is

= sqrt (k /m )

= sqrt (75 /2 )

= 6.12 rad/s

Frequenct, f = / 2*pi

                   = 6.12 / 2*3.14

                   = 0.975 Hz

Time , T = 1/f

              = 1/0.975

             = 1.026 s

b)

Max speed of body in SHM is given by

vmax = A*

where A = Amplitude of oscillation

0.45 = A * 6.12

A = 0.074 m

c)

Equation of SHM is given by

x = 0.074 cos(6.12t)

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