A spring with a 4-kg mass has natural length 0 A spring with a 4-kg mass has natural length 0.8 m and is maintained stretched to a length of 1.2 m by a force of 25.6 N. If the spring is compressed to a length of 0.6 m and then released with zero velocity, find the position x ( t ) of the mass at any time t. 1. {image} 2. 3. 4. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50
A spring with a mass of 4 kg has damping constant 32 and spring constant 128. Graph the position function of the mass at time t if it starts at the equilibrium position with a velocity of 4 m / s. 1. 2. {applet} 3. 4. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50
Suppose a spring has mass M and spring constant k and let {image} Suppose a spring has mass M and spring constant k and let {image} . Suppose that the damping constant is so small that the damping force is negligible. If an external force {image} is applied (the applied frequency equals the natural frequency), use the method of undetermined coefficients to find the equation that describes the motion of the mass. 1. {image} 2. 3. 4. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50
A series circuit consists of a resistor {image} , an inductor with L = 2 H, a capacitor with C = 0.025 F, and a 12-V battery. If the initial charge is 0.0011 C and the initial current is 0, find the current I ( t ) at time t. 1. {image} 2. 3. 4. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50
A series circuit consists of a resistor {image} , an inductor with L = 1 H, a capacitor with C = 0.0125 F, and a 12-V battery. If the initial charge and current are both 0, find the charge Q ( t ) at time t. 1. {image} 2. 3. 4. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50
A series circuit consists of a resistor {image} , an inductor with L = 1 H, a capacitor with C = 0.002 F, and a generator producing a voltage of E ( t ) = 12cos 10t. If the initial charge and current are both 0, find the charge Q ( t ) at time t. 1. {image} 2. 3. 4. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50