Question

A massless spring hangs from the ceiling with a small object attached to its lower end. The object is initially held at rest in a position yi such that the spring is at its rest length. The object is then released from yi and oscillates up and down, with its lowest position being 10 cm below yi. (a) What is the frequency of the oscillation? (b) What is the speed of the object when it is 8.0 cm below the initial position? (c) An object of mass 300 g is attached to the first object, after which the system oscillates with half the original frequency. What is the mass of the first object? (d) How far below yi is the new equilibrium (rest) position with both objects attached to the spring? 

          A massless spring hangs from the ceiling with a small object attached to its lower end. The object is initially held at rest in a position yi  such that the spring is at its rest length. The object is then released from yi and oscillates up and down, with its lowest position being 10 cm below yi.
(a) What is the frequency of the oscillation?
(b) What is the speed of the object when it is 8.0 cm below the initial position?
(c) An object of mass 300 g is attached to the first object, after which the system oscillates with half the original frequency. What is the mass of the first object?
(d) How far below yi is the new equilibrium (rest) position with both objects attached to the spring?
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Added by Catherine G.

University Physics with Modern Physics
University Physics with Modern Physics
Hugh D. Young 14th Edition
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A massless spring hangs from the ceiling with a small object attached to its lower end. The object is initially held at rest in a position yi such that the spring is at its rest length. The object is then released from yi and oscillates up and down, with its lowest position being 10 cm below yi. (a) What is the frequency of the oscillation? (b) What is the speed of the object when it is 8.0 cm below the initial position? (c) An object of mass 300 g is attached to the first object, after which the system oscillates with half the original frequency. What is the mass of the first object? (d) How far below yi is the new equilibrium (rest) position with both objects attached to the spring?
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Transcript

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00:01 The amplitude a is given by 0 .23 meter and the displacement would be given by y is equal to a divided by 2, which is equal to 0 .23 divided by 2, which is 0 .115 meter.
00:12 Now for the a part of the equation, the equation for the frequency of the oscillation would be given by f is equal to 1 divided by 2 pi multiplied by under root g divided by which is 2 .5.
00:23 1 4 multiplied by g which is 9 .81 divided by y which is 0 .115 meters.
00:30 So this would be equal to 1 .47 hires.
00:32 That's the answer for the a part of the equation.
00:34 Now for the b part of the equation we would have the equation of the frequency are f is equal to again 1 divided by 2 pi under root of g divided by y and f is equal to 1 divided by 2 pi under root g divided by y.
00:49 So from the above two equations we use the following criteria.
00:52 K divided by m is equals to g divided by y is equal to 9 .81 divided by 0 .115 meter so this would be equal to 85 .304 meter divided by second square...
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