An oscillator consists of a block attached to a spring (k = 299 N/m). At some time t, the position (measured from the system's equilibrium location), velocity, and acceleration of the block are x = 0.0817 m, v = -16.9 m/s, and a = -108 m/s2. Calculate (a) the frequency (in Hz) of oscillation, (b) the mass of the block, and (c) the amplitude of the motion.
To solve this problem, we need to use the equations of motion for a simple harmonic oscillator. Let's go step by step:
(a) The frequency (f) of oscillation can be determined using the equation:
f = 1 / (2π) * √(k / m)
Where:
k is the spring constant (299 N/m), and
m is the mass of the block (unknown).
By rearranging the equation, we can solve for m:
m = k / (4π²f²)
Substituting the known values into the formula:
m = 299 N/m / (4π²f²)
(b) To determine the mass of the block, we need the value of frequency (f). Unfortunately, this information is not provided. Make sure you have all the necessary information to solve the problem.
(c) The amplitude (A) of the motion can be determined using the equations:
A = |x_max|
Where:
x_max is the maximum displacement of the block.
Given that the position of the block is x = 0.0817 m, we can assume that it represents the maximum displacement (x_max):
A = |0.0817 m| = 0.0817 m
Therefore, the amplitude of motion is 0.0817 m.