A 0.45 kg block oscillates back and forth along a straight line on a frictionles

Question

A 0.45 kg block oscillates back and forth along a straight line on a frictionless horizontal surface. Its displacement from the origin is given by
x = (12 cm)cos[(17 rad/s)t + p/2 rad]
(a) What is the oscillation frequency (in Hz)? (b) What is the maximum speed acquired by the block? (c) At what value of x does this occur? (d) What is the magnitude of the maximum acceleration of the block? (e) At what positive value of x does this occur? (f) What force, applied to the block by the spring, results in the given oscillation?
Give your answers in centimeter-based units, where applicable.

Explanation / Answer

The mass of the block m = 0.45 kg The dispalcement of the block x = 12cm cos [(17 rad/s) t + (/2 rad)] (a) The angular frequency                   = 17 rad/s                    2f = 17 rad/s then the frequency                 f = 17 / 2 = 2.7 Hz (b) The maximum speed                             v max = A = (12 cm) (17 rad/s)                                   = 2.04 m/s (c) The maximum value is occur at mean position so the dispalcement is zero (d) The maximum acceleration       a max = A^2                  = (0.12 m) (17)^2 = 34.68 m/s^2 (e) The acceleartion should be maximum at extrem positions    so the position x = A = 12 cm (f) The force on the block             F = ma = (0.45 kg) (34.68 )                          = 15.6 N

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