Faiyaj_lab 6_attempt 1

There are three particles of mass m connected to each other and to the walls by (light) springs as shown in the figure, and they oscillate in the horizontal direction. The common spring constant of the spring is k. The deviations of the first, second, and third particles from their equilibrium positions are x,y, and z, respectively. There is no air resistance and no friction. A) Write down Newton's 2nd law for each particle B) Determine the angular frequencies (frequencies) of the non-obvious normal mode solutions. C) State the eigenstates corresponding to the normal modes using the frequencies you found m m

PART A. Simple Pendulum Fill in the table with your gathered data. Note that when computing always use raw data, but answers in the table must be round off to the specified place values. Answers must be numerical values only and must have no comma or space between numbers. Table 1. Simple Pendulum Mass: 1.00 kg Total time (s) Period T (s) Square of the Period T2 (s2) Length of Pendulum l(m) 25 oscillations Round off to hundredths place (2 decimals) Round off to hundredths place (2 decimals) Round off to tenths place (1 decimal) 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00

Q1. Consider a spring mass system given in Fig 1 with mass of 1kg attached to a spring with K=10. The motion is damped with C=6 and is being driven by a force given by 25 cos 4t . If the spring is released from rest, find the equation of displacement y(t). Note: You cannot use the direct formulas for constants in particular solution. Spring Mass r(t) Dashpot Fig. 1

M

A particle of mass m is executing the damped oscillations. Which of the following statements regarding the damped oscillations are true? 1. The amplitude of underdamped oscillations decays exponentially with time. 2. The trajectory of the particle executing the overdamped oscillations decreases monotonically to zero. 3. In overdamped oscillations, the particle overshoots the origin multiple times if the motion towards the origin is relatively quick. 4. The weak damping limit in the damped oscillations is 0,7→∞0. Here, is the angular frequency of undamped oscillations and is relaxation time. Select the correct answer choice: (a) 1 and 2 (b) 2 and 4 (c) 1,3, and 4 (d) 1,2, and 4

Conceptual Problem 4.Suppose you are inside a train where you cannot see what is going on outside. All the windows are covered with black thick cover. You cannot hear the vibrations between the tracks and the train. You don’t have any gadgets/ devices with you and you only have your student ID. Is it possible to know and distinguish if the train is moving at a constant speed or at rest? Explain or justify.

An astronaut uses a Body Mass Measurement Device to measure her mass.   Part A If the force constant of the spring is 3000 N/m, her mass is 62 kg, and the amplitude of her oscillation is 1.5 cm, what is her maximum speed during the measurement? Express your answer to two significant figures and include appropriate units.

A block oscillating on a spring has period T = 2.4 s . Note: You do not know values for either m or k. Do not assume any particular values for them. The required analysis involves thinking about ratios. a)What is the period if the block's mass is quadrupled?  b)What is the period if the value of the spring constant is doubled? c)What is the period if the oscillation amplitude is halved while

Two pendula are shown in the figure. Each consists of a solid ball with uniform density and has a mass M. They are each suspended from the ceiling with massless rod as shown in the figure. The ball on the left pendulum is very small. The ball of the right pendulum has radius 1/2 L.Randomized Variables L = 1.3 m a) Find the period T of the left pendulum for small displacements in s.  b) Find the period T of the right pendulum for small displacements in s.

A 0.300 kg oscillator has a speed of 92.4 cm/s when its displacement is 2.50 cm and 64.9 cm/s when its displacement is 5.50 cm. Part A What is the oscillator's maximum speed? Express your answer with the appropriate units. Umax = Submit μÅ Value Request Answer C Units ?

Task 2): A common example of base excitation is caused by a vehicle motion along a bumpy road surface as shown in Figure 2. This motion produces a displacement input to the suspension system via the wheels. The second task is to calculate and draw displacement transmissibility ratio diagram for a quarter car with 250 kg, the spring constant is 10000 N/m, but varying damping constant to be 1000, 2000, 3000, 5000 and 10000 N.s/m. If the vehicle driver wishes to reduce the vehicle's body displacement, what suggestion you could make for the driver and why? m X y Đ Figure 2 k Base

Calendar A or B day Logic Games - Bra... Modeling with sinusoidal functions: phase shift A pendulum is swinging next to a wall. The distance from the bob of the swinging pendulum to the wall varies in a periodic way that can be modeled by a trigonometric function. The function has period 0.8 seconds, amplitude 6 cm, and midline H = 15 cm. At time t = 0.5 seconds, the bob is at its midline, moving towards the wall. Find the formula of the trigonometric function that models the distance H from the pendulum's bob to the wall after t seconds. Define the function using radians. H(t) = Report a problem Stuck? Watch a video or use a hint. Do 4 problems

The bob on a simple pendulum is pulled to the left 4in. from its equilibrium position. After release, the pendulum makes one complete back-and-forth cycle in 2 sec and follows simple harmonic motion.                                                                                                                                                                                                                                 1. Write a function to model the displacement d (in inches) of the bob as a function of the time t (in seconds) after release.  Assume that the displacement to the right of the equilibrium position is positive.                                                                                       2.Find the position and direction of movement of the bobo at t = 1.25 sec.

Part 2

I want handwritten solutions. Please don't provide AI-generated solutions.

A and B questions which I couldn't solve . Please answer this with in 30 mins .Thank you !

A cell of mass (M) moves to the top and is attached to a Corona virus of mass (m) by a neglected thread of mass (r), where the virus oscillates at an angle, as shown in the figure. Required: 1- What are the generalized coordinates that can describe cell movement with this virus? 2- Find the Lagrange function for this inauspicious collective movement? Find the differential equation that can describe this Motion Human Cell Y

Determine the equation of motion of a damped mass spring system with each of the following data in (a) and (b) parts. Also interpret physically.

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?

A 2.41 kg the ball is attached to an unknown spring and allowed to oscillate. The figure (Figure 1) shows a graph of the ball's position x as a function of time t. Part A For this motion, what is the period? Part B What is the frequency? Part C What is the angular frequency? Part D What is the amplitude? Part E What is the force constant of the spring?

A spring with spring constant k = 12 slug/s2 has a mass attached that stretches the spring 2-2/3 ft. The damping coefficient is 7 slug/s. The mass is pushed 1 ft above the rest position and then released with a velocity of 1 ft/s downward. set up the differential equation that describes the motion under the assumption of this section. Solve the differential equation. State whether the motion of the spring system is harmonic, damped oscillation, critically damped oscillation, or overdamped. If the motion is overdamped oscillation, rewrite in the amplitude-phase form.

1 A tank contains 460 gallons of water and 10 oz of salt. Water containing a salt concentration of (1+ -sin t) oz/gal flows into the 2 tank at a rate of 6 gal/min, and the mixture in the tank flows out at the same rate. The long-time behavior of the solution is an oscillation about a certain constant level. What is this level? What is the amplitude of the oscillation? Round the values to two decimal places. Oscillation about a level = i oz Amplitude of the oscillation = i Oz.

5A = Material point of mass m moves under the influence of force F-kr = –krî With in other words, the mass m is at the tip of an isotropic harmonic oscillator with equilibrium position at the origin of the axes. a) Calculate the potential energy V(r) of m. b) To design qualitatively 1) the potential energy V(r) of the mass m, 2) its "centrifugal" dynamic energy (r) = 1² /2mr² where L is the measure of angular momentum of the mass m and r its distance from the origin of the axes, and 3) the active potential energy of U(r) = V (r)+ Vä(r). "

The springs only stretch and compress in a linear way. They do not twist nor bend. 1. Determine the degree of freedom of the system. 2. Determine the displacement vector and mass matrix of that dimension. 3. List all possible modes of vibration and explain the reason why they occur qualitatively with diagrams.

A simple harmonic oscillator (SHO) with a mass of 47 kg has a total energy of 3394 J. Determine how fast the SHO is moving when its potential energy is 3 times its kinetic energy. Express your answer using appropriate mks units. v=

When you drive your car over a bump, the springs connecting the wheels to the car compress. Your shock absorbers then damp the subsequent oscillation, keeping your car from bouncing up and down on the springs. (Figure 1) shows real data for a car driven over a bump. We can model this as a damped oscillation, although this model is far from perfect. Part A Estimate the frequency in this model. Express your answer with the appropriate units. HÀ ? f = Value Units Submit Request Answer Part B Figure 1 of 1 Estimate the time constant in this model. Express your answer with the appropriate units. HA Ay (cm) T = Value Units 0.5 t (s) 1.0 Request Answer Submit -4-

Differential Equation problem

A mass of 562 g stretches a spring by 6.9 cm. The damping constant is c = 0.37. The spring is set in motion from its equilibrium position with zero velocity. What is the w real part of the complex root of the homogeneous equation? Use g=9.8 Express your answer in two decimal places. Moving to another question will save this response. Question 2 of 10