An oscillator consists of a block attached to a spring (k = 500 N/m). At some time t, the position (measured from the system's equilibrium location), velocity, and acceleration of the block are x = 0.660 m, v = -12.3 m/s, and a = -128 m/s2. (a) Calculate the frequency of oscillation. Hz (b) Calculate the mass of the block. kg (c) Calculate the amplitude of the motion.

a) , b) , c)

Explanation:

a) The system have a simple armonic motion, whose position function is:

The velocity function is determined by deriving the position function in terms of time:

The acceleration function is found by deriving again:

Let assume that . The following nonlinear system is built:

System can be reduced by divinding the second and third expressions by the first expression:

Now, the last expression is divided by the first one:

b) The mass of the block is:

c) The phase angle is:

The amplitude is:

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explanation:

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