A object attached to a spring moves without friction (b=0) and is driven by an external force given by the expression , where F is in Newton’s and t is in seconds. The force constant of the spring is . Find
(a) The resonance angular frequency of the system,
(b) The angular frequency of the driven system, and
(c) The amplitude of the motion.
(c) The amplitude of the motion is A = 5.09 cm.
The given data can be listed below as,
Amplitude of driven oscillator with no damping is given by:
We have to find the resonance angular frequency of the system:
By using concept and formula from step (1), we get
Referring to subparts (a) and (b) of the SID: 947271-15-15.7-947271-15-53P-a and 947271-15-15.7-947271-15-53P-b
Substitute all the value in the above equation,
Hence the amplitude of the motion is A = 5.09 cm.
You attach a block to the bottom end of a spring hanging vertically. You slowly let the block move down and find that it hangs at rest with the spring stretched by 15.0 cm. Next, you lift the block back up to the initial position and release it from rest with the spring unscratched. What maximum distance does it move down? (a) 7.5 cm (b) 15.0 cm (c) 30.0 cm (d) 60.0 cm (e) The distance cannot be determined without knowing the mass and spring constant.
Review: A large block P attached to a light spring executes horizontal, simple harmonic motion as it slides across a frictionless surface with a frequency . Block B rests on it as shown in Figure and the coefficient of static friction between the two is . What maximum amplitude of oscillation can the system have if block B is not to slip?
Your thumb squeaks on a plate you have just washed. Your sneakers squeak on the gym floor. Car tires squeal when you start or stop abruptly. You can make a goblet sing by wiping your moistened finger around its rim. When chalk squeaks on a blackboard, you can see that it makes a row of regularly spaced dashes. As these examples suggest, vibration commonly results when friction acts on a moving elastic object. The oscillation is not simple harmonic motion, but is called stick-and-slip. This problem models stick-andslip motion.
A block of mass m is attached to a fixed support by a horizontal spring with force constant k and negligible mass (Fig. P15.80). Hooke’s law describes the spring both in extension and in compression. The block sits on a long horizontal board, with which it has coefficient of static friction and a smaller coefficient of kinetic friction The board moves to the right at constant speed v. Assume the block spends most of its time sticking to the board and moving to the right with it, so the speed v is small in comparison to the average speed the block has as it slips back toward the left.
(a) Show that the maximum extension of the spring from its unstressed position is very nearly given by mg/k.
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