Physics, 05.07.2019 01:20 satwikap3304
The position x of a mass m attached to a spring obeys the differential equation i + yi + w? x = 0 where y 2w. a) (2 marks) write down expressions for the forces on the mass due to (i) the spring, and (ii) damping. (3 marks) using a trial solution x = ae"', show that a = --y/2 ± (y2/4 - «2)1/2 b) c) (4 marks) show, by finding wd, that the solution is a damped oscillation of the form xc ace/2 cos(wat + pc) after some time to the mass is driven by applying a force that varies sinusoidally with frequency wf. the differential equation for x becomes i+ yx + w? x = ao cos(wft p). apcos(wft d) (6 marks) show by substitution that xp p) is a particular solution, provided that ap and pp satisfy certain conditions. find the two equations that they must satisfy. (nb: you need not explicitly solve for ap and pp.) e) (3 marks) draw a qualitative plot illustrating the dependence of ap on wf. indicate how your plot would change if y were increased. f) (2 marks) write down the general solution for x(t), and explain how this encompasses the initial transient behaviour of the mass when the driver is switched on, as well as the long term behaviour. the position x of a mass m attached to a spring obeys the differential equation i + yi + w? x = 0 where y 2w. a) (2 marks) write down expressions for the forces on the mass due to (i) the spring, and (ii) damping. (3 marks) using a trial solution x = ae"', show that a = --y/2 ± (y2/4 - «2)1/2 b) c) (4 marks) show, by finding wd, that the solution is a damped oscillation of the form xc ace/2 cos(wat + pc) after some time to the mass is driven by applying a force that varies sinusoidally with frequency wf. the differential equation for x becomes i+ yx + w? x = ao cos(wft p). apcos(wft d) (6 marks) show by substitution that xp p) is a particular solution, provided that ap and pp satisfy certain conditions. find the two equations that they must satisfy. (nb: you need not explicitly solve for ap and pp.) e) (3 marks) draw a qualitative plot illustrating the dependence of ap on wf. indicate how your plot would change if y were increased. f) (2 marks) write down the general solution for x(t), and explain how this encompasses the initial transient behaviour of the mass when the driver is switched on, as well as the long term behaviour.
Answers: 2
Physics, 22.06.2019 13:00
Aplayground merry-go-round has a radius of 4.6 m and a moment of inertia of 200 kg-m2 and turns with negligible friction about a vertical axle through its center. a child applies a 26.0 n force tangentially to the edge of the merry-go-round for 15.0 seconds. if the merry-go-round is initially at rest, how much work did the child do on the merry-go-round?
Answers: 1
Physics, 22.06.2019 16:20
What is the mass of the water that is being heated? it requires 2,500 joules to raise a certain amount of water (c = 4.186 jig c) from 20.0°c to 60.0°c. o 159 o 40 g o 63 g o 80 g
Answers: 2
Physics, 22.06.2019 21:50
Ajoint produces movement when its angle decreases. which type of movement is it?
Answers: 1
Physics, 22.06.2019 22:00
What would people living along the coast in south florida do if there was a hurricane warning? move to locations away from the water flock along coasts to watch the natural phenomenon buy instruments to predict the exact location of the hurricane measure water levels to know the exact time of the hurricane
Answers: 3
The position x of a mass m attached to a spring obeys the differential equation i + yi + w? x = 0 wh...
Social Studies, 09.04.2020 20:20
Physics, 09.04.2020 20:20
Mathematics, 09.04.2020 20:20
Mathematics, 09.04.2020 20:20
Mathematics, 09.04.2020 20:20
Computers and Technology, 09.04.2020 20:20
Biology, 09.04.2020 20:20
History, 09.04.2020 20:20
Chemistry, 09.04.2020 20:20
Chemistry, 09.04.2020 20:20
Social Studies, 09.04.2020 20:20