A spring mass oscillator consists of a spring of constant 2500 N/m and a mass 1 kg. The amplitude of the oscillator's motion is 0.17 meters. What...

A spring-mass oscillator will undergo simple harmonic motion (SHM). Such motion can be explained by the following equations:

`x = Acos(omegat + phi)`

`v = -omega A sin(omegat+phi)`

where, x (displacement from the equilibrium position) = 0.136 m, 

A (amplitude) = 0.17 m

and, `omega = sqrt(k/m) = sqrt(2500/1) = 50 (rad)/s`

substituting the values of various parameters in the equation of displacement, we get:

`0.136 = 0.17 cos(omegat + phi)`

solving this equation, we get, `omegat + phi = 0.644 radians`

or, `omegat + phi = 5.64 radians`

substituting this value in the equation of velocity, we get:

`v = -50 xx 0.17 sin(0.644)`

solving this equation, we get, v = - 5.1 m/s.

Another solution for velocity, v = `-50 xx 0.17 sin(5.64)`

or, v = 5.1 m/s.

Speed  = magnitude of velocity = 5.1 m/s

Thus, the mass of 1 kg is moving at a speed of 5.1 m/s when it is at a distance of 0.136 m from the equilibrium position. Note that mass can have a velocity of either 5.1 m/s or -5.1 m/s at the given displacement, depending on the direction of motion (towards or away from the equilibrium). However, speed is only a scalar quantity and does not have a direction. Hence the speed of the mass at that particular displacement (x = 0.136 m) is 5.1 m/s.

Hope this helps.