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- A mass weighting 40 lbs stretches a spring 3 inches. The mass is in a medium that exerts a viscous resistance of 10 lbs when the mass has a velocity of 2 ft/sec. Suppose the object is displaced an additional 4 inches and released. Find an equation for the object's displacement, u(t), in feet after t seconds. u(t) =The magnitude of the restoring force (F) and the extension (x) of a certain spring are related by: F=kx F (N) Slope=11.9 N/m x (m) Where k is the spring constant. If the theoretical value of k is: (kth=14.0 N/m). What is the percentage error in the measured value of k ? 01.0.15% O 2.0.07% O3.-15% O 4.15%The diameter of a car's suspension spring decreases uniformly. The force exerted by the spring is given by F = axb. Consider a suspension spring that compresses x1 = 12.4 cm with a 1,000 N load and x2 = 34.0 cm with a 5,000 N load. (Due to the nature of this problem, do not use rounded intermediate values in your calculations—including answers submitted in WebAssign.) (a) Find the constants a (in units of N/mb) and b. a= b= (b) Calculate the work (in J) needed to compress the spring 24.0 cm. (Assume the spring is not initially compressed.) J
- A mass weighting 64 lbs stretches a spring 6 inches. The mass is in a medium that exerts a viscous resistance of 9 lbs when the mass has a velocity of 6 ft/sec. Suppose the object is displaced an additional 7 inches and released. Find an equation for the object's displacement, u(t), in feet aftert seconds. u(t) =If the volume of liquid decreases by 0.5% for an increase of pressure from 9751987 N/m² to 251000 kN/m², calculate the bulk modulus of elasticity of the liquid. Please answer in SI unit (even temperature) with no decimals.A mass weighting 56 lbs stretches a spring 8 inches. The mass is in a medium that exerts a viscous resistance of 28 lbs when the mass has a velocity of 4 ft/sec. Suppose the object is displaced an additional 4 inches and released. Find an equation for the object's displacement, u(t), in feet after t seconds. u(t) = Question Help: Video Submit Question
- A 7-lb collar is attached to a spring and slides without friction along a rod in the vertical plane. The spring has a constant 3.5 lb/in and 15-in. undeformed length. The dimensions are: h = 15 in. The collar is moving to the left at v = 2 in/s in the position shown. Determine the force exerted by the rod on the collar at (a) point A, (b) point B. Both A and B are on the curved portion of the rod. h LA h B h hA 6-lb weight is suspended from a spring having a stiffness k = 3 lb/in. If the weight is given an upward velocity of 20 ft/s when it is 2 in. above its equilibrium position, determine the equation which describes the motionand the maximum upward displacement of the weight, measured from the equilibrium position. Assume positive displacement is downward.An object is placed on the end of a vertical spring, with a spring constant of 484.1 N/m. The spring is stretched by 0.09 m. Calculate the mass of object.
- A mass of 5 kg stretches a spring 20 cm. The mass is acted on by an external force of 10 sin () N (newtons) and moves in a medium that imparts a viscous force of 3 N when the speed of the mass is 3 cm/s. If the mass is set in motion from its equilibrium position with an initial velocity of 7 cm/s, formulate the initial value problem describing the motion of the mass. (Use g = 9.8 m/s2 for the acceleration due to gravity. Let u(t), measured positive downward, denote the displacement in meters of the mass from its equilibrium position at time t seconds. Use up for u' and upp for u".) u(0) = 0 m, u'(0) m/s =A mass of 2 kg stretches a spring 10 cm. The mass is acted on by an external force of 10 sin(2t) N and moves in a medium that imparts a viscous force of 2 N when the speed of the mass is 6 cm/s. If the mass is set in motion from its equilibrium position with an initial velocity of 2 cm/s, find the displacement of the mass, measured in meters, at any time t.A mass of 18 kilograms stretches the spring 0.3 meters. Use this information to find the spring constant (use g = 9.81 m/s² as the acceleration of gravity). k = 588 The previous mass is detached from the spring and a mass of 14 kilograms is attached. This mass is displaced 0.7 meters below equilibrium and then launched with an initial velocity of 1 meters/second. Find the equation of motion. Note: When solving this problem, consider positions below equilibrium to be positive. x(t) =