5BL Pre-Lab 4 Submission Template - F23

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Physics

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Jan 9, 2024

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5±L Pre-Lab 4 ²ssignment [Sama Suliman], [10/29/2023], [Lab °1] <URNK] SPVS]VSkjURNKLI ALILIVS]TQ x_nmpj jNKkjfg_]kjNKkj _] NKAJUR kj[VSLINK kjAsruNK mlURVSkj Akj A +±" SPVS[NK A]LI nmpfg[_ALI VSml ml_ x_nmpj #jALINKkjJ_fgNK AkjkjVSTQ]\NK]ml
° 1. ² hanging spring is stretched by 0.2 m when a mass of 0.5 kg is attached to it. The mass is then pulled down a further 0.1 m and released from rest. a)What is the angular frequency of the resulting oscillations? Show your work. b)³ow many seconds does it take for the system to go through exactly 10 complete oscillations? Show your work. g= 10m/s^2 mg= kx 0.5*10=k*0.2 k=25N/m w'#"$ sqrt ±°²³´µ²¶ w'#"$!µ´! rad³s ;Ten 6Oscillations t'#"$´µ"# ·¸´ t'#"$"µ# sec One Oscillation T=2(pi/w) T= 2*(pi/7.07) T=0.89s
¹ 2. Taking y = 0 as the initial equilibrium position of the mass in Question 1, and y > 0 upwards, write down an equation for the time dependence y(t), giving the numerical values of any constants in the solution. m=0.5 g=9.8m/s^2 x=0.2 k=mg/x k=0.5*9.8/0.2 k=24.5 N/m ²mplitude of Oscillation a=0.1m w'#"$ ±k³m¶^½ w'#"$ ±°ºµ²³´µ²¶^½ w'#"$ ! rad³sec y±t¶'#"$ a :Sin±w·t»pi³°¶ y±t¶'#"$ ´µ¸ · :Sin±!·t»pi³°¶
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º 3. What is the velocity of the mass in Questions 1 and 2 as it oscillates through the equilibrium point y = 0? (³int: you could use your solution to Question 2 to get this, or equivalently you could use conservation of energy) y±t¶ '#"$ ´µ¸·:Sin±!·t»pi³°¶ v'#"$d³dt ±y±t¶ v'#"$´µ¸·!cos±!·t»pi³°¶ v'#"$ ´µ!·cos±!t»pi³°¶ Vmax'#"$'&(·w Vmax'#"$ ´µ¸ ·! Vmax'#"$ ´µ!m³s k'#"$+-F³x k'#"$m·g³x k'#"$±´µ²·# µ"¶³° k'#"$°ºµ² 7P*,E max '#"$ K*,E max ½ k'&(^°'#"$¸³°mv max ^° ½ °ºµ²·´µ¸^°'#"$ ¸³°´ ·´µ²·v max ^° Vmax'#"$ ´µ!m³s
² 4. ´n the case of a pendulum system, what quantity in the system is oscillating in time? What physical parameters could you change in the system that might change the oscillation frequency? (i.e. what could you investigate if you didn’t know the answer.) .0In a pendulum system the piece at the bottom of the pendulum is what is oscillating over timeµ .0It swings back and forth connected to the pivot point at the topµ .0It swings in a periodic motion over and over againµ -/How frequently it oscillates can be changed in a few waysµ .0If you make the piece at the bottom of the pendulum heavier then it will oscillate slower due to the increase in weightµ .0If you make the pendulum string longer then it will also oscillate slower because there¼s more distance between the pivot and the weightµ ,.Gravity also plays a very large role and can change how it swings since it is the main force acting on itµ

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