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The total energy of a mass–spring system is the sum of its kinetic and potential energy:
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- A mass attached to a spring has non-constant acceleration a(t) = - cos ((pi*t)/4) * m / (s ^ 2) where t is time measured in seconds. If the initial velocity is zero, v\{0\} = 0m / s then what is the net change in position from t = 0 and t = 3 s? Give a numeric answer rounded to two decimal places.arrow_forwardPlease solve the problem from the information given in the problem: The equation for the line of best fit was determined to be y=0.038sin(9.56t+0.20)−0.09, where t is time in seconds and y is displacement in meters. The team used a 1 kilogram mass which displaced the spring 0.09 meters below equilibrium. We can use their initial conditions of y(0)=−0.083 and the fact that the spring was released from rest – thus y′(0)=0. Your job is to build the equation of motion for this spring. The damping coefficient c is unknown, but can you make a decent estimate for the value of c? Please consider whether the spring should be under/over/critically damped based on what you understand ofthe context. This can help you determine a value, or at least a range of possible values, for c. Compare and contrast the two displacement models. What caused the differences? Which one do you think is better?arrow_forwardThe planet Earth, Jupiter, the Moon, and the Sun have the following values: mJ = 1.90x1027kg , mE = 5.97x1024kg , mM = 7.35x1022 kg , mS = 1.99x1030kg RJ = 6.99x107 m , RE = 6.37x106 m, RM = 1.74x106 m , RS = 6.96x108 m dEarth to Moon = 3.60x105 km , dEarth to Jupiter = 588x106m , dEarth to Sun = 150x106 km (a) Find the magnitude of the force of gravity acting on the planet Earth due to the planet Jupiter. (b) Find the potential energy between the planet Earth and the planet Jupiter. (c) Find the acceleration of gravity on the planet Jupiter.arrow_forward
- Using the result of the previous question, find the value of l1, if it is given that the first pendulum swings back and forth 10 times per minute, while the second one swings back and forth 300 times per hour and l2 is 2.6 m. Give your answer in SI units. Answer: Choose... +arrow_forwardAt the park you see a child swinging. You notice it takes about 4.1 seconds for the child to make one complete swing (to return to their starting point). What is the period of the swing? (Report to 2 decimal places, and include the symbol for the unit of measure.For example, if the unit is meters, the symbol is m.)arrow_forwardSuppose the oscillatory motion of an object can be modeled using the equation s(t) = 7.8sin(3.8t) where time is measured in seconds and distance is measured in inches. Find the number of cycles (oscillations) the object makes per second. (Provide 4 decimal places.)arrow_forward
- A 10-kg steel ball is tied to a string attached to a ceiling. If the length of the string is 45 cm, a) what is the time it would take the steel ball to complete one cycle? b) If the mass of the metal ball is doubled, what will be its period?Note: Answer it using GAFSA Format (Given, Asked, Formula, Solution, Answer)arrow_forwardThe equation for the line of best fit was determined to be y=0.038sin(9.56t+0.20)−0.09, where t is time in seconds and y is displacement in meters. The team used a 1 kilogram mass which displaced the spring 0.09 meters below equilibrium. We can use their initial conditions of y(0)=−0.083 and the fact that the spring was released from rest – thus y′(0)=0. Your job is to build the equation of motion for this spring. The damping coefficient c is unknown, but can you make a decent estimate for the value of c? Please consider whether the spring should be under/over/critically damped based on what you understand of the context. This can help you determine a value, or at least a range of possible values, for c. Compare and contrast the two displacement models. What caused the differences? Which one do you think is better?arrow_forwardLet there be a mass M = 0.5 kg on a spring. a) If we can hang the mass on the spring in a vertical position, how can we measure the spring constant, k, of the spring? Now we use this same spring in the horizontal configuration, assuming the mass slides on a frictionless horizontal surface. b) Assuming we have measured k to be 10 N/m, how many times will the system oscillate in a minute? (assume we displace the mass from equilibrium so that the system oscillates) c) If the mass passes through the equilibrium position with a velocity vo at time t = 0, what is the amplitude of the oscillation? d) Write the equation for the horizontal displacement of the block as a function of time.arrow_forward
- A group of astronauts, upon landing on planet X, performed a simple pendulum experiment in the MHS (Single Harmonic Movement, Small Amplitude) regime with length L=1,1132 m. In the experiment, the pendulum performs n=9 complete oscillations at t=13,5459 s. Calculate the gravity acceleration of planet X at the experiment location. Give your answer to 4 decimal places.arrow_forwardA 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) =arrow_forwardA mass weighing 24 pounds, attached to the end of a spring, stretches it 4 inches. Initially, the mass is released from rest from a point 8 inches above the equilibrium position. Give the initial conditions. (Use g = 32 ft/s² for the acceleration due to gravity.) x(0) x'(0) x(t) = = = Find the equation of motion. ft ft ft/sarrow_forward
- Principles of Physics: A Calculus-Based TextPhysicsISBN:9781133104261Author:Raymond A. Serway, John W. JewettPublisher:Cengage Learning