A force of 720 newtons stretches a spring 4 meters. A mass of 45 kilograms is attached to the end of the spring and is initially released from the equilibrium position with an upward velocity of 6 m/s. Find the equation of motion.\[ x(t) = -6 \cdot \sin(2t) \, \text{m} \]

Force applied F= 720 N Spring stretched = 4m Mass attached m= 45kg Velocity v= 6m/s

Answered: A force of 720 newtons stretches a…

Physics for Scientists and Engineers: Foundations and Connections

1st Edition

ISBN:9781133939146

Author:Katz, Debora M.

Publisher:Katz, Debora M.

Chapter16: Oscillations

Section: Chapter Questions

Problem 28PQ: We do not need the analogy in Equation 16.30 to write expressions for the translational displacement...

See similar textbooks

Similar questions

A vibration sensor, used in testing a washing machine, consists of a cube of aluminum 1.50 cm on edge mounted on one end of a strip of spring steel (like a hacksaw blade) that lies in a vertical plane. The strips mass is small compared with that of the cube, but the strips length is large compared with the size of the cube. The other end of the strip is clamped to the frame of the washing machine that is not operating. A horizontal force of 1.43 N applied to the cube is required to hold it 2.75 cm away from its equilibrium position. If it is released, what is its frequency of vibration?
An object of mass m is hung from a spring and set into oscillation. The period of the oscillation is measured and recorded as T. The object of mass m is removed and replaced with an object of mass 2m. When this object is set into oscillation, what is the period of the motion? (a) 2T (b) 2T (c) T (d) T/2 (e) T/2
A block of mass m = 2.00 kg is attached to a spring of force constant k = 500 N/m as shown in Figure P7.15. The block is pulled to a position xi = 5.00 cm to the right of equilibrium and released from rest. Find the speed the block has as it passes through equilibrium if (a) the horizontal surface is frictionless and (b) the coefficient of friction between block and surface is k = 0.350. Figure P7.15
A grandfather clock has a pendulum length of 0.7 m and mass bob of 0.4 kg. A mass of 2 kg falls 0.8 m in seven days to keep the amplitude (from equilibrium) of the pendulum oscillation steady at 0.03 rad. What is the Q of the system?
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 = n/12, n/8, n/6, a/4, and 97/32 s. (Use g = 32 ft/s? for the acceleration due to gravity.) X(1/12) = -0.33 X ft x(x/8) = -0.66 X ft x(л/6) %3 -0.33 X ft x(T/4) = 0.66 X ft x(9x/32) = 0.47 X ft (b) What is the velocity of the mass when t = 37/16 s? 16 ft/s 3 In which direction is the mass heading at this instant? upward downward (c) At what times does the mass pass through the equilibrium position? 16 4 X , n = 0, 1, 2, +
A 1.8 kg mass attached to a horizontal spring oscillates at a frequency of 2.1 Hz. At t =0 s, the mass is at x= 2 m and has vx =− 3 m/s. What is the total energy (in Joules)?
A 10.2 gram mass is attached to an ideal spring with a spring constant 30 N/m. The mass is displaced 5.55cm from equilibrium position. What is the maximum velocity of the mass in m/s? Answer to the nearest hundredth. For example 4.26784 m/s would be 4.27m/s
A mass weighing 20 pounds stretches a spring 6 inches. The mass is initially released from rest from a point 9 inches below the equilibrium position. (a) Find the position x of the mass at the times t = £/12, ñ/8, ñ/6, ñ/4, and 9/32 s. (Use g = 32 ft/s² for the acceleration due to gravity.) X(π/12) = x(π/8)= = X(π/6) = X(π/4) = x(9л/32) = ft ft/s ft ft ft ft (b) What is the velocity of the mass when t = 3л/16 s? In which direction is the mass heading at this instant? downward upward (c) At what times does the mass pass through the equilibrium position? n = 0, 1, 2, ...
An undamped spring-mass system with a mass weighing 9 lb and a spring constant of 6 lb/in is set in motion at t = 0 by an external force of 4 cos 9t lb. Find the position u (in feet) at any time t (in seconds). u(t) = Assume that acceleration due to gravity is 32ft/s².
A vibrating spring supports a mass of 200 g and vibrates at frequency 3.95 Hz. If we replace this mass with one equal to 380 g, calculate what the new frequency of oscillation will be.
A 5.75-kg mass stretches a vertical spring 0.5 m. If the spring is stretched an additional 1.0 m and released, how long does it take to reach the (new) equilibrium position again? (What equation(s) can I use to solve this equation?)
A package of mass mmm = 6.00 kgkg is released on a 53.1∘∘ incline, a distance DDD = 4.00 mm from a long spring with force constant 1.10×102N/m1.10×102N/m that is attached at the bottom of the incline (Figure 1). The coefficients of friction between the package and incline are μsμs = 0.400 and μkμkmu_k = 0.200. The mass of the spring is negligible. (a) What is the maximum compression of the spring? (b) The package rebounds up the incline. When it stops again, how close does it get to its original position? (c) What is the change in the internal energy of the package and incline from the point at which the package is released until it rebounds to its maximum height? a) Find the magnitude of the friction force that acts on the package. Assume for the remainder of this problem that the +x direction points down along the surface of the incline, and the +y direction points away from the incline perpendicularly. Express your answer with the appropriate units. b) Using the general energy…

SEE MORE QUESTIONS

Recommended textbooks for you

Physics for Scientists and Engineers: Foundations…

Physics

ISBN:

9781133939146

Author:

Katz, Debora M.

Publisher:

Cengage Learning

Principles of Physics: A Calculus-Based Text

Physics

ISBN:

9781133104261

Author:

Raymond A. Serway, John W. Jewett

Publisher:

Cengage Learning

Classical Dynamics of Particles and Systems

Physics

ISBN:

9780534408961

Author:

Stephen T. Thornton, Jerry B. Marion

Publisher:

Cengage Learning

Physics for Scientists and Engineers: Foundations…

Physics

ISBN:

9781133939146

Author:

Katz, Debora M.

Publisher:

Cengage Learning

Principles of Physics: A Calculus-Based Text

Physics

ISBN:

9781133104261

Author:

Raymond A. Serway, John W. Jewett

Publisher:

Cengage Learning

Classical Dynamics of Particles and Systems

Physics

ISBN:

9780534408961

Author:

Stephen T. Thornton, Jerry B. Marion

Publisher:

Cengage Learning

SEE MORE TEXTBOOKS

A force of 720 newtons stretches a spring 4 meters. A mass of 45 kilograms is attached to the end of the spring and is initially released from the equilibrium position with an upward velocity of 6 m/s. Find the equation of motion. x(t) =-6- sin(21) x m