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January 30, 2015

January 30, 2015

Posted by **Anonymous** on Sunday, January 9, 2011 at 8:09pm.

x = (13 cm)cos[(20 rad/s)t + π/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?

How do you even start this problem? Please help

- physics -
**Damon**, Sunday, January 9, 2011 at 8:32pmfirst 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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