Question

1) a) A 1-kg mass stretches a spring 20 cm. The system is attached to a dashpot that imparts a damping force equal to 14 times the instantaneous velocity of the mass. Find the equation of motion if the mass is released from equilibrium with an upward velocity of 3 m/sec. b) Solve the initial value problem for the RLC circuit when R = 4?, L = 1H, C = 0.005F, v = 34 exp –t if 0 < t < 4 and 0 if t > 4. Assume zero initial charge and current 2) Reduce the following differential equations into system of first order differential equations and hence solve it using (i) Matrix method (ii) Diagonalization method a) y''+3y'+2y=0 b) y'''+2y''-y'-2y=0 3) a) A 2-kg mass is attached to a spring with spring constant 24N/m. The system is then immersed in a medium imparting a damping force equal to 16 times the instantaneous velocity of the mass. Find the equation of motion if it is released from rest at a point 40 cm below equilibrium. b) A 16-lb weight stretches a string 3.2 ft. Assume the damping force on the system is equal to the instantaneous velocity of the mass. Find the equation of motion if it is released from rest at a point 9 in. below equilibrium.

          1)
a) A 1-kg mass stretches a spring 20 cm. The system is attached to a dashpot that imparts a damping force equal to 14 times the instantaneous velocity of the mass. Find the equation of motion if the mass is released from equilibrium with an upward velocity of 3 m/sec.
b) Solve the initial value problem for the RLC circuit when R = 4?, L = 1H, C = 0.005F, v = 34 exp –t if 0 < t < 4 and 0 if t > 4. Assume zero initial charge and current

2) Reduce the following differential equations into system of first order differential equations and hence solve it using (i) Matrix method (ii) Diagonalization method
a) y''+3y'+2y=0
b) y'''+2y''-y'-2y=0

3)
a) A 2-kg mass is attached to a spring with spring constant 24N/m. The system is then immersed in a medium imparting a damping force equal to 16 times the instantaneous velocity of the mass. Find the equation of motion if it is released from rest at a point 40 cm below equilibrium.
b) A 16-lb weight stretches a string 3.2 ft. Assume the damping force on the system is equal to the instantaneous velocity of the mass. Find the equation of motion if it is released from rest at a point 9 in. below equilibrium.

1)
a) A 1-kg mass stretches a spring 20 cm. The system is attached to a dashpot that imparts a damping force equal to 14 times the instantaneous velocity of the mass. Find the equation of motion if the mass is released from equilibrium with an upward velocity of 3 m/sec.
b) Solve the initial value problem for the RLC circuit when R = 4?, L = 1H, C = 0.005F, v = 34 exp –t if 0 < t < 4 and 0 if t > 4. Assume zero initial charge and current

2) Reduce the following differential equations into system of first order differential equations and hence solve it using (i) Matrix method (ii) Diagonalization method
a) y”+3y'+2y=0
b) y”'+2y”-y'-2y=0

3)
a) A 2-kg mass is attached to a spring with spring constant 24N/m. The system is then immersed in a medium imparting a damping force equal to 16 times the instantaneous velocity of the mass. Find the equation of motion if it is released from rest at a point 40 cm below equilibrium.
b) A 16-lb weight stretches a string 3.2 ft. Assume the damping force on the system is equal to the instantaneous velocity of the mass. Find the equation of motion if it is released from rest at a point 9 in. below equilibrium.

Added by Erin K.

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