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Chapter 16 Solutions
Physics for Scientists and Engineers: Foundations and Connections
- For each expression, identify the angular frequency , period T, initial phase and amplitude ymax of the oscillation. All values are in SI units. a. y(t) = 0.75 cos (14.5t) b. vy (t) = 0.75 sin (14.5t + /2) c. ay (t) = 14.5 cos (0.75t + /2) 16.3arrow_forwardWhich of the following statements is not true regarding a massspring system that moves with simple harmonic motion in the absence of friction? (a) The total energy of the system remains constant. (b) The energy of the system is continually transformed between kinetic and potential energy. (c) The total energy of the system is proportional to the square of the amplitude. (d) The potential energy stored in the system is greatest when the mass passes through the equilibrium position. (e) The velocity of the oscillating mass has its maximum value when the mass passes through the equilibrium position.arrow_forwardAn M = 12.3 kg mass is suspended on a k = 273000 N/m spring. The mass oscillates up-and-down from the equilibrium position Yeq = 0 according to y(t) = A sin(wt + $0). Calculate the angular frequency w of the oscillating mass. Answer in units of s-¹. S At time to = 0 the mass happens to be at yo = 19.8 cm and moving upward at velocity vo +58.4 m/s. (Mind the units!) Calculate the amplitude A of the oscillating mass. Answer in units of cm. CHOOSE Calculate the initial phase do. Answer in range 0 0 < 360°. Answer in units of ᵒ. Calculate the position of the oscillating mass at the time t = 0.0662 s. Answer in units of cm.arrow_forward
- Your answer is partially correct. A particle with a mass of 1.7 x 10-20 kg is oscillating with simple harmonic motion with a period of 4.9 × 10-5 s and a maximum speed of 1.3 x 10° m/s. Calculate (a) the angular frequency and (b) the maximum displacement of the particle. (a) Number 129000 Units rad (b) Number i 0.01 Units m Save for Later Attempts: 1 of 3 used Submit Answerarrow_forwardMaps O New Tab 5. A pendulum consists of a solid sphere of radius R = 10.0 cm and mass M = 90.0 kg attached to a rod of mass m = 30.0 kg and length L. The pendulum swings freely about an axis o perpendicular to the rod and the solid sphere's center, as shown in the figure. If the pendulum is to have a period of 2.47 s for small oscillations. (a) what is the length of the rod L? (b) If the system is pulled aside to angle 0 = 67° and released, what is the maximum value for the angular velocity?arrow_forwardChapter 15, Problem 049 GO The angle (with respect to the vertical) of a simple pendulum is given by e = 0mcos[(4.40 rad/s)t + p]. If at t = 0, 0 = 0.0200 rad and de/dt = -0.160 rad/s, what are (a) the phase constant p and (b) the maximum angle 0m? (Hint: Don't confuse the rate de/dt at which e changes with the w of the SHM.) Pivor point L. Is= Le F,cose Fgsine- (a) (6) (a) Number Unit (b) Number the tolerance is +/-2% Unit Click if you would like to Show Work for this question: Open Show Workarrow_forward
- A spring of negligible mass stretches 3.00 cm from its relaxed length when a force of 7.50 N is applied. A 0.500-kg particle rests on a frictionless horizontal surface and is attached to the free end of the spring. The particle is displaced from the origin to x = 5.00 cm and released from rest at t = 0. (a) What is the force constant of the spring? (b) What are the angular frequency v, the frequency, and the period of the motion? (c) What is the total energy of the system? (d) What is the amplitude of the motion? (e) What are the maximum velocity and the maximum acceleration of the particle? (f) Determine the displacement x of the particle from the equilibrium position at t = 0.500 s. (g) Determine the velocity and acceleration of the particle when t = 0.500 s.arrow_forwardA physical pendulum composed of a solid sphere with radius R = 0.500 m, 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 forsmall angles of oscillation? The moment of inertia of the pendulum about its axis of rotation is I = 22/5 mR^2.arrow_forwardConsidering an undamped, forced oscillator (b = 0), show that equation (1) is a solution of equation (2). (1) x = A cos(wt + ¢) d²x EF = ma → Fo sin wt – bOK – kx = m9 dt? xp dt Use an amplitude given by the following equation. (Submit a file with a maximum size of 1 MB.) Fo A V (w? - w,3)? + marrow_forward
- A 1.75−kg particle moves as function of time as follows: x = 4cos(1.33t+π/5)where distance is measured in metres and time in seconds.(a) What is the amplitude, frequency, angular frequency, and period of this motion?(b) What is the equation of the velocity of this particle?(c) What is the equation of the acceleration of this particle?(d) What is the spring constant?(e) At what next time t > 0, will the object be:(i) at equilibrium and moving to the right,(ii) at equilibrium and moving to the left,(iii) at maximum amplitude, andarrow_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? For solid sphere Icm = 2/5 mr2. Also, why is the distance of the center of mass of the system from the point of oscillation 3R/2?arrow_forwardChapter 15, Problem 049 The angle (with respect to the vertical) of a simple pendulum is given by e = emcos[(4.96 rad/s)t ]. If at t 0.0350 rad and de/dt = -0.240 rad/s, what are (a) the phase constant o and (b) the maximum angle 8m? (Hint: Don't confuse 0, e the rate d0/dt at which 8 changes with the w of the SHM.) Pivot point 1е\ -Fcose sine (a) (b) (a) Number Unit (b) Number Unitarrow_forward
- Physics for Scientists and Engineers: Foundations...PhysicsISBN:9781133939146Author:Katz, Debora M.Publisher:Cengage LearningPrinciples of Physics: A Calculus-Based TextPhysicsISBN:9781133104261Author:Raymond A. Serway, John W. JewettPublisher:Cengage Learning