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Answer all please. Just give the answer. No need for lengthy solutions or explanations.
31 35 Answer All Please Just Give The Answer No Need For Lengthy Solutions Or Explanations 1 (220.85 KiB) Viewed 29 times
Question 31 A particle of mass m moves in the potential shown above. V(x) V=1/kx², x x < 0 V= mgx, x>0 The period of the motion when the particle has energy E is 2T√m/k √k/m 2π√/m/k+4√2E/mg² √//m/k+2√√/2E/mg² 2√2E/mg² Question 32 Find the equation of motion for the Lagrangian L = ²12²²_k²²y² + 2 * = -kxy² and ÿ = -ky x = xy² + kxy² and xÿ = −2ïỳ + kxy * = xy² – kxy² and xÿ = −2xỳ - kxy ) ï = xy² – kxy² and ÿ = -ky Question 33 The Hamiltonian of a system is given by -rt H = Pe + 1/{ mw²x² ert. 2m This describes which of the following systems? damped harmonic oscillator a system with unbounded motion harmonic oscillator anharmonic oscillator 1 pts 1 pts 1 pts
Question 34 1 pts Find the Lagrangian of the pendulum of mass m and length R attracted to the spring, the other end of which is fixed at the bottom as shown in the figure. The length of the undeformed spring is l. R 1 o o o o o o o o o o o • 111 OL=mR¹0²-mgR(1-cos) -k(R sin(0/2) - €)² L = ½ mR²0² + mgR(1 − cos 0) – k(2R sin(0/2) – l)² L = ½mR² 6² — mgR(1 − cos 0) – k(2R sin(0/2) – l)² OL= mR²0² +mgR(1- cos 0)-k(R sin(0/2) - ()² Question 35 1 pts Consider the Atwood's machine. Let x and y be the vertical position of the middle mass and right mass, respectively, with upward taken to be positive direction. 2m 2m m What are the conjugate momenta, px and Py, respectively? 3mx 5my Px = mx mý 2 + and Py + 2 2 2 mý 2 and Py 3mx + my mi 3mx mý + 2 and Py = + 5my 2 2 5mx my 2 3mx 2 + my 2 C O Px Px Px = mx + || = || = + and Py =
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