Question

In Concept Simulation 10.3 you can explore the concepts that are important in this problem. A block of mass m = 0.629 kg is fastened to an unstrained horizontal spring whose spring constant is k = 99.9 N/m. The block is given a displacement of +0.120 m, where the + sign indicates that the displacement is along the +x axis, and then released from rest. (a) What is the force (with sign) that the spring exerts on the block just before the block is released? (b) Find the angular frequency of the resulting oscillatory motion. (c) What is the maximum speed of the block? (d) Determine the magnitude of the maximum acceleration of the block.

Answer 1

Answer:

Explanation:

a) F = -kx = -99.9 * 0.12 = -11.988N

b)

$F = ma = -kx\\ a = -\frac{k}{m} x$

Using for x,v,a :

$x = A cos(\omega t + \phi)\\v = -\omega A sin(\omega t + \phi)\\a = -\omega ^{2} A cos(\omega t + \phi)\\a= - \omega ^2 x$

gives the angular frequency:

$\omega = \sqrt{\frac{k}{m} }$

ω = 12.6 1/s

c) v is max, when $sin(\omega t + \phi) = 1$:

$|v_{max}| = |-A\omega| = 0.12*12.6 = 1.512 \frac{m}{s}$

d) a is max, when $cos(\omega t + \phi) = 1$:

$|a_{max}|= |-\omega^2 A| = 12.6^2 * 0.12 = 19.05N$