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A quick heads up on You will be able to derive it soon … Enquiry: I ncrease mass ? Solve for T

A quick heads up on You will be able to derive it soon … Enquiry: I ncrease mass ? Solve for T Is amplitude a variable? Is friction a variable?.

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A quick heads up on You will be able to derive it soon … Enquiry: I ncrease mass ? Solve for T

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  1. A quick heads up on • You will be able to derive it soon… • Enquiry: • Increase mass ? • Solve for T • Is amplitude a variable? • Is friction a variable?

  2. A 4.0-kg object is attached to a spring of spring constant 10 N/m. The object is displaced by 5.0 cm from the equilibrium position and let go. What is the period of vibration?

  3. time • If the masses are all the same, which spring has the greatest spring constant? • Black • Green • Blue

  4. Oscillations Are about continuous mechanical energy transformations… Between KineticEnergy and Potential Energy The total mechanical energy is: Where A = xmax

  5. Ek and Ep

  6. v vmax -A +A Spring Period (Energy proof)

  7. -A +A Spring Period (Forces / Motion proof)

  8. A 200-g mass vibrates horizontally without friction at the end of a horizontal spring for which k = 7.0 N/m. The mass is displaced 5.0 cm from equilibrium and released. Find: a. Maximum speed m = 0.2 kg k = 7 N/m xo = 0.05 m vmax is at x = 0 then: v = 0.295 m/s

  9. b. Speed when it is 3.0 cm from equilibrium. x = 0.03 m v = 0.236 m/s

  10. c. What is the acceleration in each of these cases? F = ma = - kx a.x = 0 therefore a = 0 b.x = 0.03 m therefore = - 1.05 m/s2

  11. Can you prove why A, B & C are incorrect…

  12. A 0.50-kg mass is attached to a spring of spring constant 20 N/m along a horizontal, frictionless surface. The object oscillates in simple harmonic motion and has a speed of 1.5 m/s at the equilibrium position. What is the total energy of the system?

  13. A 0.50-kg mass is attached to a spring of spring constant 20 N/m along a horizontal, frictionless surface. The object oscillates in simple harmonic motion and has a speed of 1.5 m/s at the equilibrium position. What is the amplitude of vibration?

  14. A 0.30-kg mass is suspended on a spring. In equilibrium the mass stretches the spring 2.0 cm downward. The mass is then pulled an additional distance of 1.0 cm down and released from rest. Calculate the total energy of the system.

  15. As shown in the figure, a long, light piece of spring steel is clamped at its lower end and a 2.0-kg ball is fastened to its top end. A horizontal force of 8.0 N is required to displace the ball 20 cm to one side as shown. Assume the system to undergo SHM when released. Find: a. The force constant of the spring F = 8 N x = 0.2 m m = 2 kg =40 N/m b. Find the period with which the ball will vibrate back and forth. SHM = 1.4 s

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