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.

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°)

Solve part e

A massless spring hangs from the ceiling with a small object attached to its lower end. The object is initially held at rest in a position yi such that the spring is at its rest length. The object is then released from y; and oscillated up and down, with its lowest position being 10 cm below Yi. a. What is the frequency of oscillation? b. What is the speed (in m/s) of the object when it is 8 cm below the initial position? c. An object of mass 340 g is attached to the first object, after which the system oscillated with half the original frequency. What is the mass (in grams) of the first object? d. How far below (in cm) Yi is the new equilibrium (rest) position with both objects attached to the spring?

Help in C

A physics department has a Foucault pendulum, a longperiod pendulum suspended from the ceiling. The pendulum has an electric circuit that keeps it oscillating with a constant amplitude. When the circuit is turned off, the oscillation amplitude decreases by 50% in 22 minutes. What is the pendulum’s time constant? How much additional time elapses before theamplitude decreases to 25% of its initial value?

Kindly do all, if not possible then do last as many as you can

A weight is suspended from a spring and is moving up and down in a simple harmonic motion. At start, the weight is pushed up 7 cm above the resting position, and then released. After 15 seconds, the weight reaches again to its highest position. a. Find the equation of the motion b. How high is the weight with respect to the resting position after 20 seconds since it was released.

1. Find the equation of motion for a forced harmonic oscillator with Lagrangian = mx ² - 1/mo ² x ² L=-mx Here a is a constant. + ax

1. Once upon a time there was a lonely mass of 9.07185 kg suspended in thea spring. Its loneliness is furtheg aggravated by stretching the spring 3 inches. This resulted to set the upper end of the spring is then given a motion of y= 4(sin2t +cos2t). Determine: a. Equation of the motion b. The position when t=5s. 2. Eudora is observing a certain circuit consists of an inductance of 0.05 henry having a resistance of 20 ohm. Also. a condenser record a capacitance of 100 microfarads with a voltage supply of 100 cos200t V. Find the equation for q and į at steady state condition. 3. Joey a happy pendulum having a length of 6 inches is release with a velocity of 0.5 rad's toward to the vertical. from a position 1/5 rad from the vertical. Determine the equation of motion.