The discussion centers on the concept of amplitude in simple harmonic motion (SHM) as applied to two different spring problems from Halliday and Resnick. In the first problem, a spring is stretched 10 cm, but the amplitude is stated as 5 cm. In the second problem, a spring is initially stretched 9.6 cm and then displaced an additional 5 cm, with the amplitude also given as 5 cm. The participants clarify that the amplitude is defined by the initial forced displacement, not the total stretch of the spring.
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Are those the full problem statements?MenchiKatsu said:In question 37 of halliday and resnick a spring at rest length is pulled 10 cm down. And the answer say its amplitude is 5 cm. Okay. But then in question 73 a spring is stretched 9.6 cm by being hung from a weight, and then another 5 cm by hand. But this time the amplitude is 5 cm. Why ?
Those are two different problems. Can you solve them?MenchiKatsu said:A vertical spring stretches 9.6 cm when a 1.3 kg block is hung from its end. (a) Calculate the spring constant.This block is then displaced an additional 5.0 cm downward and released from rest. Find the (b) period, (c) frequency, (d) amplitude, and (e) maximum speed of the resulting SHM.
And the other one is:
A massless spring hangs from the ceiling with a small ob-ject attached to its lower end.The object is initially held at rest in a position yisuch that the spring is at its rest length. The object is then released from yiand oscillates up and down, with its lowest position being 10 cm below yi. (a) What is the frequency of the os-cillation? (b) What is the speed of the object when it is 8.0 cm be-low the initial position? (c) An object of mass 300 g is attached to the first object, after which the system oscillates with half the origi-nal frequency.What is the mass of the first object? (d) How far be-low yiis the new equilibrium (rest) position with both objects at-tached to the spring?
I don't see that assumption.MenchiKatsu said:Yes I can solve them. But that's not the question. In the second question it is assumed that the amplitude is 5 cm.
Read the question carefully. That's not the forced initial displacement.MenchiKatsu said:There's is nothing to calculate. It's just given. But shouldn't it be 10 ?
That's the initial forced displacement - which determines the amplitude.MenchiKatsu said:And it's the same for the first one. 5 cm amplitude is stated. It's not calculated.