1 The position of an object that is oscillaing on an idel sp

1) The position of an object that is oscillaing on an idel spring is glven by the equation Attire t = 0.851 s, (a) how fast is the object moving? (b) what is the magnitude of the acceleration of the object? on of an object that is oscillating on an ideal spring is given by the equation x = (12.3 ) cost(1.62s-10]. 2) For a spring stretched past its elastic regime, Hooke\'s Law no longer holds. As a toy model, we can consider a material whose force changes with displacement as F--A(1-), where A and B are constants that characterize the material. Find that the unstretched spring has zero potential energy the potential energy for this spring, as a function of the displacement, assuming 1 of 2

Solution

the position of the object is given by

    x = (12.3 cm)cos((1.62 s^-1)t)

the ve;ocity is calculated as follows:

dx/dt = -(1.62 s^-1)(12.3 cm) sin((1.62 s^-1)t)

        v = -(19.926 cm/s)sin((1.62 s^-1)t)

the acceleration of the object is,

    dv/dt = -(1.62 s^-1)^2(12.3 cm) cos((1.62 s^-1)t)

      a = -(32.28 cm/s^2)cos((1.62 s^-1)t)