Concept explainers
Consider a graphical representation (Fig. 12.3) of
Figure 12.3 (Quick Quiz 12.2)
An x–t graph for a particle undergoing simple harmonic motion. At a particular time, the particle’s position is indicated by Ⓐ in the graph.
Want to see the full answer?
Check out a sample textbook solutionChapter 12 Solutions
Principles of Physics: A Calculus-Based Text
- C, N A uniform plank of length L and mass M is balanced on a fixed, semicircular bowl of radius R (Fig. P16.19). If the plank is tilted slightly from its equilibrium position and released, will it execute simple harmonic motion? If so, obtain the period of its oscillation.arrow_forwardRefer to the problem of the two coupled oscillators discussed in Section 12.2. Show that the total energy of the system is constant. (Calculate the kinetic energy of each of the particles and the potential energy stored in each of the three springs, and sum the results.) Notice that the kinetic and potential energy terms that have 12 as a coefficient depend on C1 and 2 but not on C2 or 2. Why is such a result to be expected?arrow_forwardFigure 12.4 shows two curves representing particles undergoing simple harmonic motion. The correct description of these two motions is that the simple harmonic motion of particle B is (a) of larger angular frequency and larger amplitude than that of particle A, (b) of larger angular frequency and smaller amplitude than that of particle A, (c) of smaller angular frequency and larger amplitude than that of particle A, or (d) of smaller angular frequency and smaller amplitude than that of particle A. Figure 12.4 (Quick Quiz 12.3) Two xt graphs for particles undergoing simple harmonic motion. The amplitudes and frequencies are different for the two particles.arrow_forward
- For a simple harmonic oscillator, which of the following pairs of vector quantities can't both point in the same direction? (The position vector is the displacement from equilibrium.) velocity and acceleration position and acceleration position and velocityarrow_forwardA block of mass M = 5.4 kg, at rest on a horizontal frictionless table, is attached to a rigid support by a spring of constant k = 6000 N/m. A bullet of mass m = 9.5 g and velocity of magnitude 630 m/s strikes and is embedded in the block. Assuming the compression of the spring is negligible until the bullet is embedded, determine (a) the speed of the block immediately after the collision and (b) the amplitude of the resulting simple harmonic motion.arrow_forwardA simple harmonic oscillator consists of a spring with a force constant of k = 59.5 N/m connected to a block with a mass of m = 1.05 kg. Assume that the surface supporting the block is flat and frictionless, and there is no air resistance. At time t = 0, the spring is stretched 16.5 cm from its natural length and the block is moving at a speed of 1.95 m/s in the −x direction, as shown below. (a) Find x(t), the displacement of the block from equilibrium as a function of time. Hint: you’ll need to find the constants ω (in rad/s), A (in cm), ? (in radians) for the function: x(t) = Acos(ωt + φ). (b) What is the velocity of the block (in m/s) at t = 2.00 s? (c) What is the acceleration of the block (in m/s2) at t = 2.00 s?arrow_forward
- For a simple harmonic oscillator with x=Asinωt write down an expression for the magnitude of acceleration.arrow_forwardFind the least positive value for simple harmonic motion for t when d=0 d=1/12sin14pi(t) 1/12 1/6 12 1/14 14arrow_forwardIf a frictionless spring mass system is set into simple harmonic motion, when will the total energy in the system be equal to 1/2mv2? Answer 2) If a frictionless spring mass system is set into simple harmonic motion, when will the total energy in the system be equal to 1/2kx2? Answer 3) Hooke's law is F = - kx. What would happen if F = + kx? Which direction would F point? Answer 4) If F=ma and F=-kx2, write an equation for a in terms of m, x, and k Answer 5) Ultrasound of intensity 1.50×102 W/m2 is produced by the rectangular head of a medical imaging device measuring 3.00 by 5.00 cm. What is its power output Answer 6) A bat uses ultrasound to find its way among trees. If this bat can detect echoes 1.00 ms apart, what minimum distance between objects can it detect?arrow_forward
- The maximum velocity attained by the mass of a simple harmonic oscillator is 10 cm/s, and the period of oscillation is 2 s. If the mass is released with an initial displacement of 2 cm, find (a) the amplitude, (b) the initial velocity, (c) the maximum acceleration, and (d) the phase angle.arrow_forwardsimple harmonic oscillator consists of a block of mass 2.00 kg attached to a spring of spring constant 100 N/m.When t = 1.00 s, the position and velocity of the block are x= 0.129 m and v = 3.415 m/s. (a) What is the amplitude of the oscillations? What were the (b) position and (c) velocity of the block at t = 0 s?arrow_forwardA physical pendulum composed of a solid sphere with radius R = 0.500m, is hanged from a ceiling by string of length equal to radius. What are the (a) angular frequency, (b) period, (c) frequency of the system for small angles of oscillation? The moment of inertia of the pendulum about its axis of rotation is I= 2/5 mR^2arrow_forward
- Principles of Physics: A Calculus-Based TextPhysicsISBN:9781133104261Author:Raymond A. Serway, John W. JewettPublisher:Cengage LearningClassical Dynamics of Particles and SystemsPhysicsISBN:9780534408961Author:Stephen T. Thornton, Jerry B. MarionPublisher:Cengage LearningPhysics for Scientists and Engineers: Foundations...PhysicsISBN:9781133939146Author:Katz, Debora M.Publisher:Cengage Learning