Part V: Solve Question 2 Part VI: Solve Questions 2 & 3 Part V (30 points each): Solve ONE of the following. and solve an IVP in order to receive any credit. In each problem you must complete...
Part V (30 points each): Solve ONE of the following. and solve an IVP in order to receive any credit. In each problem you must completely set up 1. A 1000 liter tank initially contains 600 liters of salt water with 50 grams of salt dissolved in it. Salt water flows into the tank at a rate of 2 liters/hr with a concentration of 6 grams/liter and a well mixed solution leaves at a rate of 4 liters/hr. Determine how much salt is in the tank after 10 hours. 2. A 100 kg object is dropped off the bridge with an initial velocity of 2m/s downwards. If the object experiences air resistance of 400v and it hits the ground after falling for 50 seconds. How high was the bridge off the ground? Part VI (25 points each) : Answer TWO of the following. 1. A 12 kg object will stretch a spring 6cm by itself. A damper is hooked up to the system and it experiences critical damping. A force of F(t)-15sin (at) is hooked up to the system and if there was no damping the system would experience resonance. If the mass is initially displaced 15 cm downwards and given an initial velocity of 10 cm/sec upwards set up, but do not solve, and IVP for the displacement of the object at any time t. Go)(-9) 2. Find the inverse transform of the following in terms of g): F(s) s2+9 3. Find and classify all the equilibrium points for the differential equation : y'-(y-1)(y + 2)
Part V (30 points each): Solve ONE of the following. and solve an IVP in order to receive any credit. In each problem you must completely set up 1. A 1000 liter tank initially contains 600 liters of salt water with 50 grams of salt dissolved in it. Salt water flows into the tank at a rate of 2 liters/hr with a concentration of 6 grams/liter and a well mixed solution leaves at a rate of 4 liters/hr. Determine how much salt is in the tank after 10 hours. 2. A 100 kg object is dropped off the bridge with an initial velocity of 2m/s downwards. If the object experiences air resistance of 400v and it hits the ground after falling for 50 seconds. How high was the bridge off the ground? Part VI (25 points each) : Answer TWO of the following. 1. A 12 kg object will stretch a spring 6cm by itself. A damper is hooked up to the system and it experiences critical damping. A force of F(t)-15sin (at) is hooked up to the system and if there was no damping the system would experience resonance. If the mass is initially displaced 15 cm downwards and given an initial velocity of 10 cm/sec upwards set up, but do not solve, and IVP for the displacement of the object at any time t. Go)(-9) 2. Find the inverse transform of the following in terms of g): F(s) s2+9 3. Find and classify all the equilibrium points for the differential equation : y'-(y-1)(y + 2)