Module 15 Lab 12 Simple harmonic motion

Two blocks and three springs are configured as shown in the figure below. All motion is horizontal. When the blocks are at rest, all springs are unstretched. k1 m2 Suppose m, = 2m , m2 = m , k̟ = 4k , kz = k , k = 2k. Find the characteristics frequencies for small oscillations. Find out the normal modes of the oscillation.

A package is being vibrated on a vibration table. Accelerometers are attached to the table and the product to measure their accelerations. The accelerations recorded are illustrated in the plot below. Answer the following questions. Explain your answers for full credit. a. Which is greater, the forcing frequency or the natural frequency? b. Does the product bounce? c. Is the package vibrating at the same frequency as the table?

Chapter 15, Problem 058 For a damped oscillator with a mass of 240 g, a spring constant 130 N/m and a damping coefficient of 62 g/s, what is the ratio of the amplitude of the damped oscillations to the initial amplitude at the end of 21 cycles? Number Units the tolerance is +/-1 in the 2nd significant digit Click if you would like to Show Work for this question: Open Show Work

The two graphs as shown are for two different vertical mass-spring systems.a. What is the frequency of system A? What is the first time at which the masshas maximum speed while traveling in the upward direction?b. What is the period of system B? What is the first time at which the mechanical energy is all potential?c. If both systems have the same mass, what is the ratio kA/kB of their spring constants?

* Can you show me how to get the % error ? In the following table students record the time it takes for 10 cycles of the oscillating pendulum for various lengths of the pendulum. Assume the following data on the next slide is taken. Fill in all the missing entries.   Note: You don't have to do the entire table I just need a couple examples to see where I am wrong.

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A mass m is attached to a spring with spring constant k, as shown in the figure below. 0.2 m www. The mass is pulled to the right a distance of 0.2 m and released. Rank the following spring-mass combinations according to their oscillation periods from longest to shortest. If any combinations have the same period, give them the same rank. You should assume that there is no friction between the mass and the horizontal surface. (Use only ">" or "=" symbols. Do not include any parentheses around the letters or symbols.) a. k = 0.3 N/m; m = 0.10 kg b. k = 0.3 N/m; m = 0.20 kg c. k = 0.3 N/m; m = 0.40 kg d. k = 0.6 N/m; m = 0.10 kg e. k = 0.6 N/m; m = 0.20 kg

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Question #4 Can you please answer the below questions? Please do not skip any steps include ALL of your work and double check for accuracy. Thank you.

A box on a spring is pushed to point A and allowed to oscillate. Describe the motion of the box at points A, B, and C. Be sure to use the words maximum velocity, minimum velocity, maximum displacement, minimum displacement, maximum acceleration, minimum acceleration, equilibrium, and restoring force where appropriate.

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A mass m is attached to a spring with spring constant k, as shown in the figure below. 0.2 m wwww The mass is pulled to the right a distance of 0.2 m and released. Rank the following spring-mass combinations according to their oscillation periods from longest to shortest. If any combinations have the same period, give them the same rank. You should assume that there is no friction between the mass and the horizontal surface. (Use only ">" or "=" symbols. Do not include any parentheses around the letters or symbols.) a. k = 0.3 N/m; m = 0.25 kg 0.3 N/m; m = c. k = 0.3 N/m; m = d. k = 0.6 N/m; m 0.50 kg 1.00 kg 0.25 kg b. k e. k = 0.6 N/m; m = 0.50 kg

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Two blocks and three springs are configured as shown in the figure below. All motion is horizontal. When the blocks are at rest, all springs are unstretched. k1 k3 m1 m2 Suppose m, = 2m , m2 = m , k̟ = 4k , k2 = k , k3 = 2k. Find the characteristics frequencies for small oscillations.

Read the problems carefully, provide the needed values and graphs of the functions, then answer the questions that follow. Modeling: Simple Harmonic Motion A minute hand sweeps around the face of a clock once every 60 minutes. This clock has a radius of 10 cm. Write an equation for the position of the horizontal diameter of the clock (or the value of the y-coordinate of the point at the end of the minute-hand) as a function of the time in minutes. Assume that when t = 0, the minute hand is at 12. First, use the your knowledge of the 30" – 60° – 90" relationship to fill out the table for the first half of the minute hand's rotation. Then plot those values on the graph and use what you've found to finish the graph for a full rotation of the minute hand. t, in minutes 0 5 10 15 20 25 30 y, in cm What type of function will best model this situation? Why? What is the amplitude? How did you determine this? What is the period? How did you determine this? Use these answers to write an equation…

An object with a mass of 2400 g is attached to a spring with a spring constant of 360 N/m. When the object is 15 cm from its equilibrium position, it is moving with a speed of 500 cm/sec. Show all work for full credit. a. What is the amplitude? (in cm) b. What the maximum velocity the object travels? (in cm/sec)

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A spring with a spring constant of k=157N/m is initially compressed by a block a distance d=0.21m. The block is on horizontal surface with coefficient of kinetic friction yk static friction ys and has a mass of m=6kg B)Assuming the block is released from the initial position and begins to move to the right input an expression for the sum of the force in the x- direction in the configuration.

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The spring constantContext For your engineering degree, you do an internship in a mechanical component characterization company. You are currently working on determining the spring constant of industrial springs. To do this, you measure the elongation of springs placed on a graduated inclined plane, to which you attach masses. Constraints One end of the spring is attached to a hook at the top of the inclined plane and the other end is attached to a mass.The spring is parallel to the plane, the force it exerts on the mass is therefore also parallel to the plane.The angle of inclination of the plane is known, as well as its uncertainty.There is no friction between the plane and the mass.The natural length of the spring and its uncertainty are known.By hooking a known mass (m±delta m), you measure that the spring now has a length (L±delta L).We use the value g=(9.81±0.01)m/s^2 for our calculations. Schematization Draw a diagram of the object that interests us. Draw your x and y axes. Draw…

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Problem 1 An object of mass m = 0.2 kg is hung from a spring whose spring constant is 80 Nm-1. The body is subject to a resisti vity force given by -br, where v is its velocity and b = 4 Nm-. 1. Write the differential equation of motion, and specify what is the type of oscillat ion the block undergo? (Critical, under damping, over damping) 2. Determine the period of such oscillation 3. The object is subjected to a sinusoidal force given by F(t) = Fosin(wt) where Fa = 2N and w = 30rad/ sec. In steady state, what is the amplitude of forced ascillation?