11.5✶✶ (a) Find the normal frequencies, w₁ and w₂, for the two carts shown in Figure 11.15, assuming that m₁ = = m2 and k₁ = k2. (b) Find and describe the motion for each of the normal modes in turn. Problems for Chapter 11 449 k₂ k₁ m ma X1 x2 Figure 11.15 Problems 11.5 and 11.6. 11.6** Answer the same questions as in Problem 11.5 but for the case that m₁ = m2 and k₁ = 3k2/2. (Write k₁ = 3k and k₂ = 2k.) Explain the motion in the two normal modes.

1. Sinewave A lags sinewave B by 30°. Both have peak values of 15V. Sinewave A is the reference with a positive going crossing at 0º. Determine the instantaneous value of sinewave B at 30°, 45°, and 2000. 2. Make a sketch of two sinewaves as follows. Sinewave A is the reference and sinewave B lags A by 90°. Both have equal amplitudes.

The position 7 (in meters) of a particle of mass m (in kilograms) is described as two perpendicular oscillations that are out of phase with each other: 7 = rēi + yế2 = cos(wt)ěi + cos(wt + ø)ē2, where o is the constant phase angle difference. a. Show that the position 7 of the particle satisfies the harmonic oscillator equation -w?r. dt? Compute the particle's velocity v = dr/dt, dot product 7 · v, and angular momentum L = mĩ x v. Is the angular momentum constant in both magnitude and direction? b. Set w = 2 rad / s and ø = T/3 rad. Make a table with the following columns: t, x, y, Væ, Vy, and7· v. Put the units beside their respective variables and enclose the units inside the parentheses. Set the initial time to be to = 0 and use the spreadsheet to compute the values of xo, Yo, VOx, VOy, and ro · vo Write down the spreadsheet formula for the first xo, Yo, VOz, VOys and 7o - vo , assuming that the initial time to is spreadsheet cell A2.

A 4.00 [kg] frictionless block is attached to an ideal spring of force constant 400.[N/m]. At ? = 0 the block has velocity -5.00 [m/s] and displacement 0.200 [m].  Now solve for this:  A. The amplitude of the oscillation B. The position-time and velocity-time functions of the spring-mass system Need help thank you.

can you pls help me solve this.. our topic is Oscillations. 1. A simple pendulum of length 3m is set into simple harmonic motion at an angle 20 degrees. Determine: a) Amplitude of the wave (A = Ltheta) b) period (T = 2pi radical length / g) c) Angular frequency (w = radical k/m = radical g/l) d) Maximum velocity and acceleration of the motion (vmax = w radical A^2 - x^2  ; amax = -w^2x)   •Pls answer with complete solution (3 dec places) •Sketch an illustration/diagram with labels (this is a must; for a better understanding)   Thank you  I will give your answer a LIKE for helping me...

The differential equation for a simple harmonic oscillator is the following: x''=-ω2x True or False.x=Aeωt is a solution of the SHO equation? A. TrueB. False

HW1//: find the amplitude, period, and frequency for the following waveform. a. 20 sin 377t b. 5 sin 7541 c. 10° sin 10,000t e. -7.6 sin 43.6t d. 0.001 sin 942t f. ) sin 6.2831 HW/2 Find the phase relationship between the waveforms of cach set: a. v= 4 sin(wr + 50°) i = 6 sin(wr + 40°) b. v = 25 sin(ot - 80°) i = 5 x 10- sin(wr - 10°) c. v= 0.2 sin(wt - 60°) i = 0.1 sin(wr + 20°) d. v = 200 sin(wt i = 25 sin(wr 210°) 60°) HW/3 Repeat Problem 29 for the following sets: a. v = 2 cos(ot - 30°) i - 5 sin(wt + 60°) c. v= -4 cos(wt + 90°) i = -2 sin(wt + 10°) b. v = -1 sin(wt + 20°) i - 10 sin(wr - 70°)

Given the function f(x) – - 1 sin(z) a. Equation of midline: b. Amplitude: c. Draw the graph. -2 -72 -1 37/2 27 -2

Tarzan swings back and forth on a long vine. His friend Jane notices in amazement that he makes 30 complete swings in 2.4 minutes. a)What is the frequency (in hertz) of Tarzan's swing? b)How long is the vine he is using?

A pendulum at rest is hit to put it in motion. The distance the pendulum is from its resting position is given by the function f(t)=3esim(4t) for t20 in which t is measured in seconds and f(t) is measured in millimeters. How far is the pendulum from its resting position after 3 seconds? SC 301 *Student can enter max 3000 characters EON XO BI US ! 1 ← q a alt N @ 2 W S #m 3 X e d C $ 4 C r f Use the paperclip button below to attach files. M % s do 5 V t g Oll ^ 6 b y h V 8⁰ & 7 n J j * 00 8 O i m ( 9 k O < " alt ) 0 1 Р ^. ➜ ctrl .... { [ ? 4 + 11 1 Oct