# physics

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A 0.57 kg block oscillates back and forth along a straight line on a frictionless horizontal surface. Its displacement from the origin is given by
(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?

• physics -

first find the period. That is when the argument of the cos changes by 2 pi
when t = 0
20(0) + pi/2 = pi/2
2 pi + Pi/2 = 2 pi + pi/2
so
period when 20t = 2 pi
or T = 2 pi/20 = pi/10
f = 1/T = 10/pi

b
dx/dt = .13 (20)(-sin(20t+pi/2))
max when |sin| = 1
dx/dt max = 2.6 m/s

c
well at lots of values of x but one is when
20t+pi/2 = pi/2
or t = 0

d take the next derivative and repeat

e now you have the acceleration d^2x/dt^2
F = m a

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