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A spring hung vertically with a spring stiffness constant of
290 N/m
oscillates with an amplitude of
25.0 cm
when supporting a mass of
0.24 kg
. The mass passes through the equilibrium point
(x=0)
with positive velocity at
t=0
. A) What equation describes this motion as a function of time? B) At what times will the spring be longest and shortest?

Respuesta :

The spring will be the longest when T = 0.045 seconds has passed, and the shortest when T = 0.135 seconds has passed. For a spring hung vertically with a spring stiffness constant of 290 N/m.

The main purpose of a mechanical spring, an elastic component, is to deflect under load. As the load is relieved, returning to its original shape and location. An elastic machine component that can flex when a load is applied is the stiffness constant. It returns to its previous place after the burdens are taken away. In order to restore elasticity, a spring is a mechanical device built of a material with a very high yield strength.

Amplitude, A = 0.25m

stiffness constant = 290N/M

mass, m = 0.24kg,

angular velocity = w =(k/m)^1/2= (290/0.240)^1/2

W = 34.7 Rad/sec

For a spring at maximum stretch = 34.7t = sin^-1(1)

34.7T = 3.14

T = 3.14/2*34.2

T = 0.045sec

For a spring at minimum stretch = sin(34.7t) = -1

34.7t = sin^-1(-1) = (3*90)/2

t =3 *pi/2*34.7 = 0.135 sec

Learn more about stiffness constant here

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