maths

1. 1
Assignment-2
1
A mass weighing 2 pounds stretches a spring 6 inches. At 0t  the mass is released from a point 8 inches below the
equilibriumposition with an upward velocity of 4/3 ft/s. Determine the amplitude and frequency of the motion.
2
A mass weighing 100 N attached to the end of a spring, stretches it 10 cm. Initially, the mass is released from rest
from a point6 cm above equilibriumposition.Determine the displacementof the equation of motion.
3
Determine the displacement of the motion, if mass 1,m  spring constant 9,k  damping force 8,c  and external
force   12cos6 ,F t t and initial conditionsare    0 3, 0 0x x 
4
The motion of a mass on a certain vertical spring is described by    
2
2
50 9cos8 , 0 0, 0 3
d x
x t x x
dt
    , where x is
the distance of the mass from the equilibrium position, downward being taken as positive direction. Determine the
displacement of the motion, amplitudeand frequency of the motion.
5
A mass weighing1 pound stretches a spring 6 inches. At 0t the mass is released from a point 6 inches below the
equilibriumposition with an upward velocity of 4/3 ft/s. Determine the amplitude and frequency of the motion.
6
An 8-lb weight stretches a spring 2 ft. Assuming that a damping force numerically equal s to two times the
instantaneous velocity acts on the system, determine the motion if the weight is released from the equilibrium
position with an upward of 3 ft/sec.
7
The motion of a mass on a certain vertical spring is described by    10 100 90 0, 0 0.16, 0 0y y y y y       ,
where y is the distance of the mass from the equilibrium position, downward being taken as positive direction.
Determine the displacement of the motion.
8
A mass weighing 100 N attached to the end of a spring, stretches it 10 cm. Initially, the mass is released from rest
from a point 6 cm above equilibrium position. Determine the displacement, period, frequency and amplitude of the
equation of motion.
9
A mass of 1 slug is attached to a spring whose constant is 5 lb/ft. Initially, the mass is released 1 foot below the
equilibrium position with a downward velocity of 5 ft/s, and the subsequent motion takes place in a medium that
offers a damping force that is numerically equal to 2 times the instantaneous velocity. Determine the equation of
motion if the mass is driven by an external force equal to f(t) =12 cos 2t + 3 sin 2t.
10 Obtain the current in an RLC-circuitwhen 3
0.25 , 0.025 , 2L H C F E t V   and initially currentand chargezero.
11
Determine the steady state current of an RLC-circuit when 4 , 0.1 , 0.05 , 110cos2R L H C F E t V     and initial
current and chargezero.
12
Obtain the solution of the IVP for the charge with given data is 3
8 , 0.2 , 12.5 10 , 100sin10R L H C F E t V
     
and initial currentand chargezero.
13
Obtain the solution of the IVP for the charge with given data is 18 , 1 , 0.025 , 220cos4R L H C F E t V     and
initial currentand chargezero.
14
The motion of a mass on a certain vertical spring is described by    16 64 0, 0 0.33, 0 0x x x x x       , where x is
the distance of the mass from the equilibrium position, downward being taken as positive direction. Determine the
displacement of the motion.
15
Determine the steady state current in an RLC-circuit with negligibly small R when 0.5 , 0.005 , sinL H C F E t V  
and initial currentand chargezero.
16
Determine the current  I t in an RLC-circuit with 2
11 , 0.1 , 10 , 110sin377R L H C F E t V
     and initial
current and chargezero.
17
Determine the charge on the capacitor in an RLC-circuit when 10 , 1.6 , 0.03 , 300R L H C F E V     and initial
current and chargezero.
18
The motion of a mass on a certain vertical spring is described by    0.2 1.2 2 5cos4 , 0 0.5, 0 0y y y t y y       ,
where y is the distance of the mass from the equilibrium position, downward being taken as positive direction.
Obtain the displacement of the motion.
19
Determine the amplitude of steady state current in an RLC-circuit when 10 , 0.25 , 0.05 , sinR L H C F E t V    
and initial currentand chargezero.
20
Determine the steady state charge in an RLC-circuit when 20 , 0.5 , 0.005 ,R L H C F   
100sin60 200cos40E t t V  and initial currentand chargezero.