1. Suppose you attach an object to a vertical spring originally at rest, and let it bounce up and down. You release the object from rest at the spring’s original rest length. If the spring has a force constant of 11.1 N/m and a 0.3 kg-mass object is set in motion as described, find the amplitude of the oscillations.
2. If your heart rate is 145 beats per minute during strenuous exercise, what is the time per beat in units of seconds?
1. Spring force is given by: kx, where k is spring constant and x is compression/elongation.
Also, gravitational force is given by mg, where m is mass and g is gravitational acceleration.
For equilibrium, these forces must be balanced => kx=mg =>x=mg/k
Here,m= 0.3 kg and k= 11.1 N/m.
So,x= 0.3*9.8/11.1 = 0.265 m.
So, distance between extreme position and equilibrium position is 0.265 m => amplitude is 0.265 m
2.For 145 beats, 1 minute (=60 seconds) is required.
So, time required for 1 beat = 60/145 = 0.414 seconds.
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