Calculating Oscillatory Motion: Mass, Spring Constant, and Displacement

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The discussion focuses on a block of mass 0.900 kg attached to a spring with a spring constant of 94.5 N/m, displaced by +0.120 m before being released. The force exerted by the spring on the block just before release is calculated using Hooke's Law, F = -kx. The angular frequency of the oscillatory motion is derived from the spring constant and mass, and the maximum speed of the block is determined using the formula Vmax = A * angular frequency. Additionally, the maximum acceleration is calculated based on the angular frequency and amplitude. The thread emphasizes the importance of understanding these fundamental equations in oscillatory motion.
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A block of mass m = 0.900 kg is fastened to an unstrained horizontal spring whose spring constant is k = 94.5 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 (magnitude and direction) that the spring exerts on the block just before the block is released?
N

(b) Find the angular frequency of the resulting oscillary motion.
rad/s

(c) What is the maximum speed of the block?
m/s

(d) Determine the magnitude of the maximum acceleration of the block.
m/s2
 
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What are the equations you're looking at using for this?
 
x=Acos * angular frequency * time
Vmax=A* angular frequency
 
Here's one to start with, and should spring* to mind anytime you see a problem with a spring-- Hooke's Law:

F = -kx

relating the restoring force imparted by the spring on an object displaced from equilibrium.

*sorry, I simply couldn't resist the pun :-)
 

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