A 4 kg mass is statically suspended from a load (force) cell and the load cell deflection caused by the mass is 0.04 mm. Estimate the following: 1. The natural frequency of the load cell is equal to rad/s.
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- A mass m = 3.3 kg is at the end of a horizontal spring on a frictionless horizontal surface. The mass is oscillating with an amplitude A = 4.5 cm and a frequency f = 1.5 Hz. a. Write an equation for the spring constant k. b. Calculate the spring constant k, in Newtons per meter. c. Write an equation for the total mechanical energy, E, of the motion. Your expression should be in terms of the variables in the original problem statement. d. Calculate the total mechanical energy E, in joules.PLEASE DONT USE CHATGPT A block-spring type harmonic oscillator with k=23 N/m and m=0.47 kg has a mechanical energy of 25 mJ. a) What is the amplitude of the motion? b) What is the maximum speed of the block? c) What is the speed of the block when x=11 mm?1. If a spring has a spring constant of 23.0 N/m² then how much force is required to stretch it 11.0 cm from equilibrium? s Y91909 of a simple harmonic oscillator ever zero? If so, where?
- 3) A small sphere has radius 2cm and mas 60g. It is suspended at equilibrium from a spring with spring 14 w/m! Find how much the sphore shetches the stored in the spring. Constand and Spring the energy ^ i's pulled down an b From equilibrium, the sphere addinord Bem and released so it oscillates. up and down harmonically. Alse conservation of energy to calculate the kinetic energy to the equilibrium height. the sphere when it returns 18You attach a 2.0 kgkg object to a spring, pull it down 0.16 mm from the equilibrium position, and let it vibrate. You find that it takes 4.6 ss for the object to complete 10 vibrations. Determine the frequency of vibrations. Determine the spring constant. Determine the total energy of system Determine the maximum speed. Determine the maximum acceleration4. Under certain conditions, wind blowing past a rectangular speed limit sign can cause the sign to oscillate with a frequency w (see Fig.). Assume that w is a function of the sign width, b; sign height, h; wind velocity, V; air density, p; and an elastic constant, k, for the supporting pole. The constant, k, has dimensions of Nm. (a) Develop a suitable set of pi terms for this problem using b, V, and p as repeating variables. (b) List all the other possible combinations of repeating variables that could have been utilized for this problem. SPEED LIMIT 40
- 1) Determine the change in chemical energy each second required to produce this increase in electric potential energy. 2) If there are roughly 7×10^11 of these cells in the body, how much chemical energy is used in pumping sodium ions each second? 3) Estimate the fraction of a person's metabolic rate used to pump these ions. Assume the metabolic rate to be 100 W.Problem 4 A damper square mat is supporting a dead load weight of 8 kN. Helical springs will be used to support the load located at all corners with shearing stress of 120.6 Mpa at 20 turns. The spring has a deformation of 98.7 mm with a mean radius of 80 mm. Design the minimum diameter of the wire to support a load. Use G = 83 Gpa. %3D 8 kNthin re is measured The second harmonic frequency for a long at 200 Hz when it is attached to the ceiling with amass in tied to its bottom. Adding an extra lkg to the hanging mass increases the second harmonic Frequency to 245 M₂. Findm [draw appropriate diagrams to explain]