A massless spring with spring constant of 50N/m lies on a horizontal frictionles

Question

A massless spring with spring constant of 50N/m lies on a horizontal frictionless surface. A body of mass 0.6 kg is attached to the free end; the mass is moved so as to stretch the spring 12 cm. After being released, the mass starts moving in simple harmonic motion. 1) Write the simple harmonic equation for this system, x= Acos(wt), with the constants A and w as numbers. 2) What is the minimal time for the mass to move form a maximum positive displacement to a maximum negative displacement? 3) What is the maximum velocity of tha mass? 4) what is the maximum asseceration of the mass? 5) What is the minimum time for the mass to move from x=6cm to x=-6cm?

Explanation / Answer

1) Amplitude A = 0.12 m

    = (K/m) = 50/0.6 = 9.13 rad/sec..

x = 0.12 cos(9.13 t)

2) = 2/T = 9.13

T = 9.13 / 2 = 1.45 sec..

Time for the mass to move form a maximum positive displacement to a maximum negative displacement is equal to half of theTime period.. i.e T/2..

t = T/2 = 0.725 sec...

3) Max Velocity = A x = 0.12 x 9.13 = 1.0956 m/sec..

4) Max acceleration = A x 2 = 0.12 x 9.132 = 10 m/sec2..

5) Minimum time for the mass to move from x=6cm to x=-6cm (halves of amplitudes) is = T/4 = 1.45/4

   t1 = 0.3625 sec..

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