Breakout Problem #1 A uniform rod with mass M = 2 kg is mounted on a frictionless axle that passes through the CM. Two identical springs (k = 10 N/m) are attached to opposite ends of the rod as shown. What is the period of small angle oscillations? Use energy conservation to solve this problem. (hint: express the stretching/compression of the spring in terms of the angular position of the rod) k k
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- 1: In this question we will study the damped harmonic oscillator. Consider the following spring-mass system. kr bà Figure 1: Spring-mass system with a friction force. That is, an object of mass m is attached at the end of a spring with spring-constant k. We will also consider the effect of friction. Friction works in the opposite direction of motion, as illustrated in the figure. A) Show that the differential equation governing the damped spring-mass system is: më = -bå – kx (1) dr and i = dt where i = dt2 b) To solve the differential equation (1), we will take the following ansatz: r(t) = Ae. (2) If the above r(t) is a solution of Eq. (1) show that A has to satisfy the following equation: 1² +27d + wi = 0, (3) * and wi = k Solve the above equation to find A. m2 b where y 3= 2m c) For wi >?, show that the general solution can be written as: x(a) = Ae-t cos (wt +0) (4) where w? = w - 7². 2: Using Fermat's principle prove the law of reflection and the law of refraction of light.B/ Answer the following questions: D Define stress, strain and Hook's law, and draw their relation. 2) According to simple harmonic motion, in the moment of an object passing by the half distance of its passage then what the state of its energy? 3) if a wall clock has been fallen from a height, will it keep giving the correct time during the free fall? Explain the reason.Part A (Figure 1) shows velocity graph for an oscillation along the x-axis. What is the maximum speed of the oscillation? Express your answer to two significant figures and include the appropriate units. HÁ Value Units Umax = Submit Request Answer Figure K 1 of 1> Part B V, (cm/s) What is the frequency of the ocillation? 60 Express your answer to two significant figures and include the appropriate units. 30 µẢ t (s) 12 6. 6. -30 f = Value Units -60- Submit Request Answer 3.
- A simple pendulum of length 2.3 m makes 4.0 complete swings in 37.0 s. Part A What is the acceleration of gravity at the location of the pendulum? Express your answer using two significant figures. Π| ΑΣΦ g= Submit Provide Feedback Request Answer ? m/s²A 2.00 kg, frictionless block s attached to an ideal spring with force constant 350 N/m. At t = 0 the spring is neither stretched nor compressed and the block is moving in the negative direction at 11.0 m/s. Show Transcribed Text Part A G Find the amplitude. Express your answer to three significant figures and include the appropriate units. Show Transcribed Text Part B Go Find the phase angle. Express your answer in radians. Show Transcribed TextPart A After landing on an unfamiliar planet, a space explorer constructs a simple pendulum of length 55.0 cm. The explorer finds that the pendulum completes 96.0 full swing cycles in a time of 129 s What is the magnitude of the gravitational acceleration on this planet? Express your answer in meters per second per second. > View Available Hint(s) Tempiates Symbols undo rego Tését keyboard shortcuts Help 9planet m/s? Submit Prevlous Anawere
- Chapter 15, Problem 072 A uniform circular disk whose radius R is 14.7 cm is suspended as a physical pendulum from a point on its rim. (a) What is its period? (b) At what radial distance r < R is there a pivot point that gives the same period? (a) Number Units (b) Number Units Click if you would like to Show Work for this question: Open Show WorkOn a frictionless, horizontal air track, a glider oscillates at the end of an ideal spring of force constant 2.30 N/cm. The graph in the figure (Figure 1) shows the acceleration of the glider as a function of time. Part A Find the mass of the glider. Express your answer with the appropriate units. For related problemsolving tips and strategies, you may want to view a Video Tutor Solution of Angular frequency, frequency, and period in shm. Value Units m = Part B Find the maximum displacement of the glider from the equilibrium point. Figure Express your answer with the appropriate units. HÀ ? ar (m/s³) A = Value Units 12.0 6.0 t (s) 0/10 0.20 030 0.40 -6.0 -12.0 Part C Find the maximum force the spring exerts on the glider. Express your answer with the appropriate units.