Question

9. The differential equation for simple harmonic motion (Pr/dt -w22) can be obtained from the expression for the total energy of the system. Show that this is true for a mass-spring system. (Hint: consider the total energy equation for this system. What must its time derivative equal) Hint: What are the equations for K and U, and what does the derivative of a constant equal? 10. A small marble slides back and forth in a parabolic bowl without friction. Let be its horizontal distance from the bowl's center, and y = er be the height of the bowl. (a) Does the marble's position follow simple harmonic motion? Hint: the previous problem may help you here! "He would later be condemned and imprisoned by the Catholic church, but not for this reason. "Wait, I thought it's 24 hours Nope, it's 23:56:1.09. See this chapter in the online textbook used for Astro 1 and Astro 12 to learn why: https://openstar.org/books/astronomy/pages/4-3-keeping-time (b) At what angular frequency will the particle oscillate?

Answer 1

9. The differential equation for simple harmonic motion (Pr/dt -w22) can be obtained from the expression for the total energy of the system. Show that this is true for a mass-spring system. (Hint: consider the total energy equation for this system. What must its time derivative equal) Hint: What are the equations for K and U, and what does the derivative of a constant equal? 10. A small marble slides back and forth in a parabolic bowl without friction. Let be its horizontal distance from the bowl's center, and y = er be the height of the bowl. (a) Does the marble's position follow simple harmonic motion? Hint: the previous problem may help you here! "He would later be condemned and imprisoned by the Catholic church, but not for this reason. "Wait, I thought it's 24 hours Nope, it's 23:56:1.09. See this chapter in the online textbook used for Astro 1 and Astro 12 to learn why: https://openstar.org/books/astronomy/pages/4-3-keeping-time (b) At what angular frequency will the particle oscillate?

9. Saln! Given Differential Equation for SHD as To show that this is true for mass-sping system fooooo A Consider a spring with spoing fororront constant k' when it is a • stretched to a distance x, it can be shown that the polential energy associated = £ kx²] when the spring execute SHM, asthangular frequency is the kinetic Energy ean be given by K = m = mw² (A?x?) where Vaw JAZZ A2 Amplitude .:K= k k (A²-x²) ka mw2 Total Enagy = utk in E = kxx² + 2K (A²x²) & KA² When the spring is stretched through a distance & the restoring force developed F= -kic I . ma = -kx as X o -wx, who was the 10. a) Yes, At x' the acceleration is towards the centre of the bowl. 6) At x' U= mgh = ngxx² ( height= (x²) But u = kx² mo?= 2ngc 2 k zamge w2z2gc w = 12gc V But kamwe V et