An object of mass `0.8kg` is attached to one end of a spring and the system is set into simple harmonic motion. The displacement `x` of the object as a fuction of time is shown in the figure. With the aid of the data, determine
(a) the amplitude `A` of the motion,
(b) the angular frequency `omega`,
( c) the spring constant `K`,
(d) the speed of the object at `t = 1.0 s` and
(e) the magnitude of the object's acceleration at `t = 1.0 s`.

Answer

A, B, C, D

Explanation

(b) `omega = (2pi)/(T) = (2pi)/(4) = 1.57 rad//s`
(c ) `omega = sqrt((k)/(m))`
:. `k = m omega^(2) = (0.8)(1.57)^(2) = 1.97 N//m`
(d) At `t = 1 s`
`v = slope of x - t graph = 0`
(e) At `t = 1 s` , `x` is maximum `( = + A)`. Therefore. magnitude of acceleration is also maximum.
`a = maximum = omega^(2) A = (1.57)^(2)(0.08)`
` = 0.197 m//s^(2)`