Physics 3210Week 15 clicker questionsThe transverse displacement from equilibrium of masses on an elastic string is qjfor mass j. What is the elastic energy of the system of masses, if the spacing between masses is d and the tension is t?A. B. C. n12j 1 jj11dU q q2tD. E. n1j 1 jj11dU q q2t n12j 1 jj11U q q2dt n1j 1 jj11U q q2dt n14j 1 jj11U q q2dtIn studying the weighted elastic string, we derived the equationWhat is solution for the frequency if n=1 (one mass only)?A. B. C. 2mdt22222mdd2mddKAd2mddtt tt ttt mdt2mdtD. E.2mdtmdtA weighted string consists of regularly spaced masses (mass m, spacing d) connected by string with tension t. For each normal mode of the motion, all the masses oscillate at frequency . What is the spatial dependence of the normal mode amplitude?A. Constant amplitude for all masses.B. The amplitude is constant in magnitude but switches sign between adjacent masses.C. The amplitude decays exponentially along the string.D. The amplitude varies sinusoidally along the string.E. The amplitude varies linearly along the string.A weighted string consists of regularly spaced masses (mass m, spacing d) connected by string with tension t. For each normal mode of the motion, all the masses oscillate at frequency . Which of the normal modes sketched below has the lowest frequency?A.C.B. D.Physics 3210Wednesday clicker questionsA weighted string consists of n regularly spaced masses (mass m, spacing d) connected by string with tension t. What is the correct limit to take to get a continuous weighted string?A. n→∞B. m→0C. d→0D. A and CE. A, B, and CWhat is a good approximation toin the limit d→0?A. B. C. D. E. dsin2Lddsin2L 2Ldsin 02L2ddsin 12L 2L dsin d2Ldsin2L 2LHow does the value of the integral depend on m and ℓ?A. The integral is zero always.B. The integral is nonzero always.C. The integral is zero unless m=ℓ.D. The integral is nonzero unless m=ℓ.E. The answer depends on the value of L.L0x m xdxsin sin2L 2L What is a good approximation toin the limit d→0?A. B. C. D. E. q x q x ddqxqxqdxqdx22qxPhysics 3210Friday clicker
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