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 12:30
Awheel of mass 48 kg is lifted to a height of 0.8 m. how much gravitational potential energy is added to the wheel? acceleration due to gravity is g = 9.8 m/s2. a. 30.4 j b. 3.1 j c. 297.9 j d. 11,321 j
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Physics, 22.06.2019 17:30
Current from a charged capacitor lights a bulb. as time goes on the brightness of the
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Physics, 22.06.2019 19:20
The dipole moment of the water molecule (h2o) is 6.17x10^-30 c.m. consider a water molecule located at the origin whose dipole moment p points in the +x-direction. a chlorine ion ( of charge-1.60x10^-19c , is located at x=3.00x10^-9m . assume that is much larger than the separation d between the charges in the dipole, so that the approximate expression for the electric field along the dipole axis can be used. a) find the magnitude of the electric force that the water molecule exerts on the chlorine ion. b) what is the direction of the electric force. -x-direction or +x-direction c) is this force attractive or repulsive?
Answers: 1
The position x of a mass m attached to a spring obeys the differential equation i + yi + w? x = 0 wh...
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