Chapter 15: Q. 2 (page 415) URL copied to clipboard! Now share some education! An air-track glider is attached to a spring. The glider is pulled to the right and released from rest at t=0s. It then oscillates with a period of 2.0sand a maximum speed of 40cm/s. a. What is the amplitude of the oscillation?b. What is the glider’s position att=0.25s? Short Answer Expert verified a. The oscillation has an amplitude of 12.74cm.b. The glider’s position at t=0.25sis ∓9cm.$$\begin{aligned}&y(t)=A\cos(\omegat+\phi)\\&0=\cos\phi\\&\phi=\pm\frac{\pi}{2}\\&y=A\cos\left(\omegat\pm\frac{\pi}{2}\right)\\&=12.74\times\cos\left(3.14\times0.25\pm\frac{\pi}{2}\right)\\&=\mp9\mathrm{~cm}\end{aligned}$${"x":[[41,36,18,11,13,21,35,42,42,34,18,12],[27,24],[92,89,68,64,69,85,94,95,88,71,65],[78,78],[177,172,189,199,203,201,190,176],[213,226,239,238,231,219,212,211,216,227,235,239],[276,267,250,247,251,264,275,276,276,276,273,255,248],[285,284,291],[287,284],[300,299,299,300,308,319,329,327],[364,350,352,341,348,352,352,355,363],[400,395,383,374,372,376,387,395,399,400,400,399,400,403],[411,411,418,429],[438,437,444],[438,440],[480,472,452,452,462,476,481,480,480,480,477,457,452],[490,489,489,490,498,510,519,517],[529,542,555,554,547,535,528,527,532,543,551,555],[591,594,589,570,563,569,591],[608,617,617,617,617,628,629,617,615,615,613,606],[699,699,703,718,727,727,728,728,729,724,706,700],[757,741,741,758],[796,795,788,778,770,767,766],[767,785],[810,825,824,808],[840,866],[840,867],[882,896,896,910],[888,903],[1012,1007,993,984,987,1002,1014],[1036,1025,1022,1022,1029,1042,1050,1052,1050,1036],[1087,1086,1078,1065,1058,1064,1084,1089,1089,1085,1076,1064,1058],[1147,1131,1130,1146],[1200,1190,1186,1188,1197,1209,1215,1216,1212,1200],[1225,1224,1225,1225,1230,1240,1246,1247,1246,1246,1254,1263,1267,1265],[1276,1289,1301,1303,1291,1283,1275,1276,1282,1295,1303],[1338,1332,1314,1311,1317,1338,1339,1340,1339,1334,1318,1312],[1375,1373,1366,1355,1348,1351,1362,1371,1373,1375,1375,1375,1379],[1452,1450,1438,1429,1423,1422],[1423,1442],[1470,1509],[1490,1489],[1556,1554,1561,1571,1584,1586,1581,1570,1555],[1594,1594,1594,1594,1603,1623,1621],[1632,1631,1638],[1634,1631],[1650,1664,1667,1666,1650],[1846,1831,1830,1831,1837,1853,1858,1859,1859,1855,1846],[1874,1900],[1874,1901],[1975,1968,1950,1947,1951,1965,1977],[1997,1986,1983,1983,1990,2003,2011,2013,2011,1997],[2049,2047,2035,2023,2020,2027,2037,2048,2050,2046,2036,2024,2019],[2126,2124,2131,2141,2154,2156,2151,2140,2125],[2164,2165,2165,2164,2171,2185,2193,2192],[2201,2205],[2204,2203,2208],[2408,2406,2413,2424,2436,2438,2433,2422,2407],[2446,2446,2447,2446,2453,2469,2475,2474],[2484,2483,2490],[2484,2486],[2509,2536],[2510,2536],[2584,2582,2589,2600,2612,2614,2609,2598,2583],[2622,2623,2623,2623,2629,2638,2645,2645,2645,2645,2649,2660,2665,2663],[2760,2760,2742,2739,2739],[2759,2740],[2768,2769,2768,2769,2768,2782,2794,2797],[2832,2828,2813,2805,2807,2820,2831,2832,2833,2833,2833,2836],[2872,2867,2846,2844,2848,2869,2874],[2909,2897,2896,2894,2886,2886,2894,2895,2895,2895,2903],[2950,2948,2955,2969,2976,2980,2977,2966,2950],[2989,2988,2995],[2989,2991],[3009,3018,3018,3018,3018,3029,3030,3018,3016,3016,3014,3007],[3061,3047,3045,3047,3042,3038,3045,3047,3046,3045,3051,3060],[3070,3069,3081,3095,3100,3092,3069,3069,3100],[3110,3122,3118,3122,3128,3131,3119,3119,3119,3108],[3295,3294,3300,3310,3319,3323,3323,3323,3324,3319,3303,3295],[3343,3370],[3344,3370],[3385,3398,3399,3413],[3391,3407],[3515,3510,3496,3487,3490,3505,3517],[3539,3529,3525,3527,3536,3548,3554,3555,3551,3539],[3594,3591,3581,3570,3565,3566,3577,3588,3594,3594,3588,3575,3566,3563],[3664,3664,3671,3682],[3691,3706,3716,3718,3712,3698,3690,3690,3698,3711,3717],[3747,3746,3728,3727,3727,3726],[3746,3727],[3785,3784,3777,3767,3759,3756,3755],[3756,3774],[3814,3797,3798,3812],[3867,3856,3853,3853,3860,3873,3881,3883,3881,3867],[3892,3891,3892,3892,3898,3908,3912,3911,3912,3912,3917,3927,3934,3932],[3943,3958,3968,3970,3964,3950,3942,3942,3950,3963,3969],[4006,3998,3978,3978,3988,4002,4007,4006,4006,4006,4003,3983,3978],[4043,4038,4026,4017,4015,4019,4030,4038,4042,4043,4043,4042,4043,4046],[4119,4116,4105,4094,4090,4089],[4090,4110],[4195,4193,4200,4210,4223,4225,4220,4209,4194],[4233,4233,4234,4234,4240,4249,4257,4257,4257,4256,4263,4273,4276,4275],[4371,4371,4353,4350,4350],[4370,4351],[4379,4380,4379,4380,4379,4393,4405,4408],[4443,4439,4424,4416,4418,4431,4442,4443,4444,4444,4444,4447],[4483,4478,4457,4455,4459,4480,4485],[4520,4506,4508,4497,4504,4508,4508,4511,4519],[4561,4559,4566,4577,4589,4591,4586,4575,4560],[4600,4599,4606],[4602,4599],[4619,4632,4632,4632,4632,4639,4641,4630,4632,4629,4618],[4672,4660,4659,4657,4649,4649,4657,4658,4658,4658,4666],[4681,4680,4692,4706,4711,4703,4680,4680,4711],[4721,4733,4729,4733,4739,4742,4730,4730,4730,4719],[4782,4781,4782,4781,4781,4796,4807,4810],[4819,4818,4825],[4821,4818],[4861,4853,4833,4833,4843,4857,4862,4861,4861,4861,4858,4838,4833],[4870,4870,4870,4870,4879,4899,4897],[4937,4935,4923,4914,4908,4907],[4908,4927],[4949,4963,4966,4965,4949],[5136,5162],[5136,5163],[5178,5194,5194,5192],[5206,5206,5221,5231,5233,5220,5207,5203,5202,5233],[5245],[5258,5285,5285,5257],[5319,5319,5319,5296,5296,5326],[5423,5420,5409,5398,5394,5393],[5394,5414],[5431,5435],[5434,5433,5438],[5447,5446,5447,5447,5452,5462,5468,5469,5468,5468,5476,5485,5489,5487],[5499,5512,5525,5524,5517,5505,5498,5497,5502,5513,5521,5525],[5563,5561,5549,5537,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Step by step solution 01 Given Information (part a) Time period, T=2s.Maximum speed,v=40cm/s. 02 :Formula used (part a) Time period,T=2πω.Amplitude,A=vω.Where, ωis the angular frequency. 03 Calculation (part a) ω=2πT=2×3.142s=3.14rad/sSubstitute the values of vand ωto obtain A.A=vω=40cm/s3.14rad/s=12.74cm 04 Final Answer (part a) The oscillation has an amplitude of12.74cm. 05 Given Information (part b) Time period,T=2sMaximum speed,v=40cm/sTime,t=0.25sAngular frequency,ω=3.14rad/sAmplitude,A=12.74cmInitial condition,t=0,y=0. 06 Formula used (part b) Equation of the simple harmonic motion is y(t)=Acos(ωt+ϕ).Where, Ais the amplitude, yis the position, ωis the angular frequency and ϕis the phase. 07 Calculation (part b) y(t)=Acos(ωt+ϕ)0=cosϕϕ=cos-10ϕ=π2Then,role="math" localid="1648532252093" y=Acosωt±π2=12.74×cos3.14×0.25±π2=∓9cm 08 Final Answer (part b) At timet=0.25s, the position of the glider is∓9cm. 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