You want to construct a pendulum that has a natural frequency equal to that of a matching spring/mass combination. The desired length of the pendulum is 1.2 m and the spring constant of the only available spring you have is 100 N/m. What mass do you need for the spring in order to match the frequency of the pendulum?
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- An ideal spring hangs from the ceiling. A 1.25 kg mass is hung from the spring, stretching the spring a distance d = 0.0865 m from its original length when it reaches equilibrium. The mass is then lifted up a distance L = 0.0325 m from the equilibrium position and released. What is the kinetic energy K of the mass at the instant it passes back through the equilibrium position? K = d Equilibrium position wwwwww. wwwhow to do?A mass of 0.50 kg is held against compressed spring and released from rest while upon a horizontal, frictionless surface. The spring constant of the spring is 790 N/m and the mass leaves the spring with a speed of 7.84 m/s. Assume that the spring pushes the mass across the surface. By what amount was the spring initially compressed relative to its equilibrium position? 0.197
- A spring hangs vertically from a ceiling. The spring constant of the spring is k=15 N/m. A 2kg object has been attached to the spring and the spring has already come to its new equilibrium. Someone pulls the object down by 5cm and releases it at time t = 0s. The spring and object begin to oscillate under simple harmonic motion. Find the total energy of the system, the maximum kinetic energy, the maximum potential energy, and the positions where the maximum energies occur. Answers: 0.01875 J, 0.01875 JA 1.00-kg mass is attached to a spring hanging vertically and hangs at rest in the equilibrium position. The spring constant of the spring is 1.00 N/cm. The mass is pulled downward 2.00 cm and released. What is the speed of the mass when it is 1.00 cm above the point from which it was released? 0.0443 m/s 1.73 m/s 1.67 m/s 0.0201 m/s The mass will not reach the height specified.A mass of 0.3 kg hangs motionless from a vertical spring whose length is 0.75 m and whose unstretched length is 0.55 m. Next the mass is pulled down to where the spring has a length of 1.05 m and given an initial speed upwards of 1.7 m/s. What is the maximum length of the spring during the motion that follows? maximum length= Hint: the conceptually-simplest approach is to track the changes in kinetic, spring-potential, and gravitational-potential energies; the mathematically-simplest approach is to observe that the sole effect of gravitation is to lower the spring's equilibrium position, then track just the kinetic and spring-potential (relative to the lower equilibrium) energies.
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