A mass of 5 kg is attached to a spring with spring constant 25N/m. The mass is acted on by an external force of 10 sin(t) Newtons and moves in a medium that imparts a viscous force (i.e. friction) proportional to the velocity with constant 10Ns/m. If the mass is set in motion from its equilibrium position with an initial velocity of 60 cm/s, formulate the initial value problem describing the motion of the mass. Then solve this initial value problem. HINT: watch out for the units! Centimeters are not meters!

A mass of 5 kg is attached to a spring with spring constant 25N/m. The mass is acted on by an external force of 10 sin(t) Newtons and moves in a medium that imparts a viscous force (i.e. friction) proportional to the velocity with constant 10Ns/m. If the mass is set in motion from its equilibrium position with an initial velocity of 60 cm/s, formulate the initial value problem describing the motion of the mass. Then solve this initial value problem. HINT: watch out for the units! Centimeters are not meters!

Essentials of Business Analytics (MindTap Course List)

2nd Edition

ISBN:9781305627734

Author:Jeffrey D. Camm, James J. Cochran, Michael J. Fry, Jeffrey W. Ohlmann, David R. Anderson

Publisher:Jeffrey D. Camm, James J. Cochran, Michael J. Fry, Jeffrey W. Ohlmann, David R. Anderson

Chapter5: Probability: An Introduction To Modeling Uncertainty

Section: Chapter Questions

Problem 29P: The Siler Construction Company is about to bid on a new industrial construction project. To...

See similar textbooks

Similar questions

One kg of water within a piston-cylinder assembly executes a Carnot power cycle. During isothermal expansion, the water is heated from a saturated liquid at 50 bar until is a saturated vapor. The vapor then expands adiabatically to a pressure of 5 bar and a quality of 0.8291. a) Sketch the cycle on P-v and T-s diagram. b) Evaluate the heat transfer and wor for the above processes (isothermal expansion and adiabatic expansion) c) Evaluate the thermal efficiency.
I drag a stick at 2 m/s through an extremely shallow rectangular box filled with oil, creating a shock wave. I measure the angle made by the wave with the line along which the stick isdragged to be 45°. What is the speed of surface waves in this box?
Suppose that Motorola uses the normal distribution to determine the probability of defects and the number of defects in a particular production process. Assume that the production process manufactures items with a mean weight of 10 ounces. Calculate the probability of a defect and the suspected number of defects for a 1,000-unit production run in the following situations. a. The process standard deviation is 0.15, and the process control is set at plus or minus one standard deviation. Units with weights less than 9.85 or greater than 10.15 ounces will be classified as defects. b. Through process design improvements, the process standard deviation can be reduced to 0.05. Assume that the process control remains the same, with weights less than 9.85 or greater than 10.15 ounces being classified as defects. c. What is the advantage of reducing process variation, thereby causing process control limits to be at a greater number of standard deviations from the mean?
A consulting engineer is considering two pumps to meet a demand of 15,000 gallons/minute at 12 feet total dynamic head. The specific gravity of the liquid being pumped is 1.50. Pump A operates at 70% efficiency and costs $12,000; pump B operates at 75% efficiency and costs $18,000. Power costs $0.015/kilowatt-hour. Continuous pumping for 365 days/year is required (i.e., 24 hours/day). Using a MARR of 10% and assuming equalsalvage values for both pumps, how many years of service are required forpump B to be justified economically? (Note: Dynamic head times gallon/ minute times specific gravity divided by 3960 equals horsepower required. Horsepower times 0.746 equals kilowatts required.)
A mechanical engineer is considering two types of pressure sensors for the low-pressure steam lines in several of the company plants. Piezoresistive sensors use the change in conductivity of semiconductors to measure the pressure. Fiber optic sensors use the properties of fiber optic interferometers to sense nanometer scale displacement of membranes. The costs for each system are shown below. Which should be selected based on a present worth comparison at an interest rate of 1% per month?
If the air-conditioning system for a 200,000 ft2 building is estimated to be 400 ft2 per ton and to cost $4000 per ton, then what will be the system cost? And If, through load management, the system capacity for the building in above problem is reduced by 10%, will the system cost be reduced by 10%? If not, why?
Develop a worksheet simulation for the following problem: The management of Montemayor Manufacturing Company is considering the introduction of a new product. The fixed cost to begin the production of the product is ₱30,000. The variable cost for the product is uniformly distributed between ₱16 and ₱24 per unit. The product will sell for ₱50 per unit. Demand for the product is best described by a normal probability distribution with a mean of 1,200 units and a standard deviation of 300 units. Develop a spreadsheet simulation similar to the one provided previously. Use 500 simulation trials to answer the following questions. What is the mean profit for the simulation? What is the probability that the project will result in a loss? What is your recommendation concerning the introduction of the product?
A process control manager is considering two robots to improve materials handling capacity in the production of rigid shaft couplings that mate dissimilar drive components. Robot X has a first cost of $84,000, an annual M&O cost of $31,000, a $40,000 salvage value, and will improve revenues by $96,000 per year. Robot Y has a first cost of $146,000, an annual M&O cost of $28,000, a $47,000 salvage value, and will increase revenues by $119,000 per year. The company’s MARR is 15% per year and it uses a 3-year study period for economic evaluations. Which one should the manager select (a) on the basis of ROR values, and (b) on the basis of the incremental ROR value? (c) Which is the correct selection basis? Perform the analysis by hand or spreadsheet, as instructed.
Ned Thompson Labs performs tests on superalloys, titanium, aluminum, and most metals. Tests on metal composites that rely upon scanning electron microscope results can be subcontracted or the labs can purchase new equipment. Evaluate the sensitivity of the economic decision to purchase the equipment over a range of ±20% (in 10% increments)of the estimates for P, AOC, R, n, and MARR (range on MARR is 12% to 18%). Use the AW method and plot the results on a sensitivity graph. For which parameter(s) is the AW most sensitive? least sensitive? First cost, P = $-180,000 Salvage, S = $20,000 Life, n = 10 years Annual operating cost, AOC=$-30,000 per year Annual revenue, R = $70,000 per year MARR = 15% per year
A design engineer must select the horsepower for a motor to drive a pump. Horsepower rating is a continuous design parameter with values in the range of 10 to 40 horsepower. The motor will have an annual ownership cost of $120 plus $0.60 per horsepower. The operating costs of such motors for 1 horsepower-hour will be $0.055 divided by the horsepower rating. Nine thousand horsepower-hours will be needed per year. Solve, a. Determine what horsepower should be specified for a minimum total annual cost. b. Show that you have minimized total cost per year.
A cement grinding mill “A” with a capacity of 50 tons per hour utilizes forged steel grinding balls costing ₱ 12,000 per ton, which have a wear rate of 100 grams per ton cement milled. Another cement mill “B” of the same capacity uses high chrome steel grinding balls costing ₱ 50,000 per ton with wear rate of 20 grams per ton cement milled. Determine the more economical grinding mill, considering other factors to be the time?
Dunlop company conducts tests on tires life . For a particular tires, the standard deviation is 6000 kilometers,and the 68% of tires life failed between two values (102000 , 78000) what is the value of the mean life of dunlop tires ?