# With reference to a spring pendulum or a bob pendulum, what happens to force, acceleration, and velocity at max displacement AND at equilibrium.

valentin68 | College Teacher | (Level 3) Associate Educator

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The simple harmonic motion of a mass is described in one dimension (x) by the equation

`x(t) =A*sin(omega*t+phi)`

where the values of amplitude `A` , and initial phase `phi` can be computed from the initial conditions (values of position and speed at `t=0` ).

Consequently the values of the speed, acceleration and force are

`v(t) = dx/dt = A*omega*cos(omega*t +phi)`

`a(t) =dv/dt =-A*omega^2*sin(omega*t+phi) =-omega^2*x(t)`

`F(t) = m*a(t) =-m*omega^2*x(t)`

At equilibrium we have

`x(t) =0 => sin(omega*t+phi) =0 => cos(omega*t +phi) =1`

and the values of speed, acceleration and force are:

`v =A*omega` , `a =0 m/s^2` , `F=0 N`

At maximum displacement we have

`x(t) = A => cos(omega*t +phi) =1 => sin(omega*t + phi) =0`

and the values of speed, acceleration and force are

`v =0 m/s` , `a =-omega^2*A` , `F =-m*omega^2*A`

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