21.4 Questions 1. If a uniform spring is cut in half, what is the spring constan

Question

21.4 Questions 1. If a uniform spring is cut in half, what is the spring constant of each hal? d and se what hapn) actually cut a spring in half, but you could put two identical springs end-to-end and sere nt of each half? Justify your answer. (Don't end-to-end and see what happens...) 2. How would the frequency using a half-spring differ from that using the same mass and the entire spring? 3. For a vertical system, how does the mass of the spring change the characteristics of the system? 4. If the amplitude of an object in SHM is doubled, how would it affect the energy and maximum speed?

Explanation / Answer

let the intial spring constant is k

and the spring constant of half spring is k1

Now, we can assume that two half springs are connected in Series ,

for springs in series ,

1/k1 + 1/k1 = 1/k

2/k1 = 1/k

k1 = k/2

the spring constant of half spring is half that of original spring

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