A horizontal spring with spring constant 85 N/m extends outward from a wall just above floor level. A 5.5 kg box sliding across
a frictionless floor hits the end of the spring and compresses it 6.5 cm before the spring expands and shoots the box back out. How fast was the box going when it hit the spring
1 answer:
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Answer:
The time constant is
Explanation:
From the question we are told that
The spring constant is
The mass of the ball is
The amplitude of the oscillation t the beginning is
The amplitude after time t is
The number of oscillation is
Generally the time taken to attain the second amplitude is mathematically represented as
Here T is the period of oscillation
=>
=>
Generally the amplitude at time t is mathematically represented as
Here a is the damping constant so
at ,
So
=>
taking natural log of both sides
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Generally the time constant is mathematically represented as
=>
=>