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4. [5/7 Points] | DETAILS l PREVIOUSANSWERS l MYNOTES PRACTICEANOTHER A particle moves along the x axis. It is initially at the position 0.130 m, moving with velocity 0.220 m/s and acceleration -0.270 m/sz. Suppose it moves with constant acceleration for 3.10 s. (a) Find the position of the particle after this time. -0.48535 y m (b) Find its velocity at the end of this time interval. -0.617 y m/s We take the same particle and give it the same initial conditions as before. Instead of having a constant acceleration, it oscillates in simple harmonic motion for 3.10 5 around the equilibrium position x = 0. Hint: the following problems are very sensitive to rounding, and you should keep all digits in your calculator. (c) Find the angular frequency of the oscillation. Hint: in SHM, a is proportional to x. 1,441 /s (d) Find the amplitude of the oscillation. Hint: use conservation of energy. 0,2005 y m (e) Find its phase constant qno if cosine is used for the equation of motion. Hint: when taking the inverse of a trig function, there are always two angles but your calculator will tell you only one and you must decide which of the two angles you need. -0.87 y rad (f) Find its position after it oscillates for 3.10 5. -0.1177 x Your response differs from the correct answer by more than 10%. Double check your calculations. m (9) Find its velocity at the end of this 3.10 s time interval. -0.234 x The response you submitted has the wrong sign. m/s 5. [3/5 Points] PREVIOUS ANSWERS SERPSE10 15.2.0P.01 1.M|. PRACTICE ANOTHER A 0.520-kg object attached to a spring with a force constant of 8.00 N/m vibrates in simple harmonic motion with an amplitude of 10.6 cm. (Assume the position of the object is at the origin at t = 0.) (a) Calculate the maximum value of its speed. 41.55 a; cm/s (b) Calculate the maximum value of its acceleration. 162.88 y cm/s2 (c) Calculate the value of its speed when the object is 6.60 cm from the equilibrium position. 4.154 x Can you determine a time when the object is at this position? You can then use this time in your equation of motion. cm/s (d) Calculate the value of its acceleration when the object is 6.60 cm from the equilibrium position. 189.4 x How can you determine the force that acts on the object at this position? cm/s2 (e) Calculate the time interval required for the object to move from x = 0 to x = 4.60 cm. 00.114 w 5 Need Help? 7. [3/4 Points] DETAILS PREVIOUS ANSWERS ' SERPSE1015.A.OP.O42. MY NOTES I PRACTICE ANOTHER I A simple pendulum with a length of 1.33 m and a mass of 6.64 kg is given an initial speed of 1.76 m/s at its equilibrium position. (a) Assuming it undergoes simple harmonic motion, determine its period (in s). 2.31 J 5 (b) Determine its total energy (in J). 10.28 / J (c) Determine its maximum angular displacement (in degrees). (For large V, and/or small I, the small angle approximation may not be good enough here.) 28.20 / (d) what If? Based on your answer to part (c), by what factor would the total energy of the pendulum have to be reduced for its motion to be described as simple harmonic motion using the small angle approximation where 6 5 10? 0.866 x