A body weighing 9.25 grams force hangs from a spring stretching 1.4 centimeters. Initially the body...

A body weighing 9.25 grams force hangs from a spring stretching 1.4 centimeters. Initially the body part of rest 2.6 centimeters below its position balance. The medium where the body moves offers a resistance force to movement that is numerically equal to 1/2 of its instantaneous speed. Knowing that there is an external force, changing in time, that It is defined by the formula: f (t) = cos (t) grams force. Find the position in centimeters of the body after 3 seconds. Take positive above from the equilibrium position. Consider magnitudes towards down negative and up positive

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milcah answered 2 years ago

A body weighing 9.25 grams force hangs from a spring stretching it 1.4 centimeters. Initially the...

A body weighing 9.25 grams force hangs from a spring stretching it 1.4 centimeters. Initially the body part of rest 2.6 centimeters below its equilibrium position. The medium where the body moves offers a force of resistance to movement that is numerically equal to 1/2 of its instantaneous speed. Knowing that there is a force external, changing in time, which is defined by the formula: f (t) = cos (t) grams strength. Find the position in centimeters of the body...

DIFFERENTIAL EQUATIONS: 1. A body with a weight of 3.5 grams force hangs from a spring...

DIFFERENTIAL EQUATIONS: 1. A body with a weight of 3.5 grams force hangs from a spring stretching it 3.21 centimeters. Initially the body starts from rest 3.4 centimeters below its equilibrium position. The medium in which the body moves offers a resistance force to movement that is numerically equal to 1/8 of its instantaneous speed. Knowing that there is an external force, changing in time, which is defined by the formula: f (t) = 7cos (t) grams force. Find the...

A body weighing 2 pounds forces hangs from a spring with constant 4 lb / ft....

A body weighing 2 pounds forces hangs from a spring with constant 4 lb / ft. The medium in which the body moves offers a resistance force to movement that is numerically equal to its instantaneous speed. If the weight is released 1/3 feet above its balance position with a downward speed of 9 feet per second, determine the speed at which time it passes through the balance position. Consider negative downward and positive upward magnitudes.

A body weighing 10 pounds forces hangs from a spring with constant 4/5 lb / ft....

A body weighing 10 pounds forces hangs from a spring with constant 4/5 lb / ft. The medium where the body moves it offers a resistance force to movement that is numerically equal to its instantaneous speed. If the weight is released 5/3 feet above your balance position with a downward speed of 6 feet per second, determine the position the lower the object reaches. Consider negative downward and positive upward magnitudes

A body weighing 128 pounds hangs from a spring with constant 1400 lb/ft. The medium, where...

A body weighing 128 pounds hangs from a spring with constant 1400 lb/ft. The medium, where the body moves, offers a force of opposition to the movement numerically equal to 15 for its instantaneous speed. If the weight is released 2 feet above its balance position, say how fast it should be initially pushed so that after 6 seconds it reaches the lower limit position. Take the constant of gravity as 32 ft/sec^2.

A mass weighing 8 pounds stretches a spring 1 foot. The mass is initially released from...

A mass weighing 8 pounds stretches a spring 1 foot. The mass is initially released from rest from a point 2 feet below the equilibrium position, and the subsequent motion takes place in a medium that offers a damping force that is numerically equal to 2 times the instantaneous velocity. Find the equation of motion (solve the IVP) if the mass is driven by an external force equal to f(t) = 5 cos(2t). Graph the solution. What part of the...

A mass weighing 20 pounds stretches a spring 6 inches. The mass is initially released from...

A mass weighing 20 pounds stretches a spring 6 inches. The mass is initially released from rest from a point 8 inches below the equilibrium position. (a) Find the position x of the mass at the times t = π/12, π/8, π/6, π/4, and 9π/32 s. (Use g = 32 ft/s2 for the acceleration due to gravity.) x(π/12) = −14 ft x(π/8) = −.5 ft x(π/6) = −0.25 ft x(π/4) = 0.5 ft x(9π/32) = 0.35 ft (b) What is...

A mass weighing 12 pounds stretches a spring 2 feet. The mass is initially released from...

A mass weighing 12 pounds stretches a spring 2 feet. The mass is initially released from a point 1 foot below equilibrium with an upward velocity of 4 ft/s. (a) Find the equation of motion (b) In correct units, what are the amplitude, period, and frequency of this simple harmonic motion? (c) What is the velocity of the mass at ? = 3? 16 seconds? (d) Find the first three times that the velocity is zero, expressed both in exact...

A mass weighing 32 pounds stretches a spring 16 feet. The mass is initially released from...

A mass weighing 32 pounds stretches a spring 16 feet. The mass is initially released from rest from a point 2 feet below the equilibrium position, and the subsequent motion takes place in a medium that offers a damping force that is numerically equal to 1/2 the instantaneous velocity. Find the equation of motion if the mass is driven by an external force equal to f(t)=10cos(3t).

A mass weighing 16 pounds stretches a spring 8/3 feet. The mass is initially released from...

A mass weighing 16 pounds stretches a spring 8/3 feet. The mass is initially released from rest from a point 3 feet below the equilibrium position, and the subsequent motion takes place in a medium that offers a damping force that is numerically equal to 1/2 the instantaneous velocity. Find the equation of motion x(t) if the mass is driven by an external force equal to f(t) = 10 cos(3t). (Use g = 32 ft/s2 for the acceleration due to...

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