JSFH

Problem 1.1.6 (modified) alpha:=<lambda/2*(1/t+2*t+t^3),lambda/2*(log(1/t)+t^2+3/4*t^4)-7/8*lambda>;

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Part a) We solve x(t)=2*lambda x0:=solve(alpha[1]=2*lambda,t);

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Note that Maple found a bunch of solutions. It might be easier to understand what they are if we convert to floating point. evalf(x0);

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So there are only two real solutions, and one iteresting one at t=1. tmin:=x0[1];

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lambda:=3;

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plot([alpha[1],alpha[2]],t=1/3..3);

NigtJSdDVVJWRVNHNiQ3UzckJCIxTExMTExMTEwhIzskIjFiYmJiYmJiYiEjOjckJCIxeXh4eDJmOVIhIzskIjFAai0jSHdoNCYhIzo3JCQiMUFBQXMoUi5VJSEjOyQiMXNaeFFDMVxbISM6NyQkIjE2NjY2dTUqKVwhIzskIjFhTChwSGYmKm8lISM6NyQkIjA2NjZAWDtjJiEjOiQiMjAnPkkhZiZlQlkhIzs3JCQiMSopKSkpKVE9WUpoISM7JCIxMCl6SDAvO2olISM6NyQkIjFXV1clemEoZm0hIzskIjEkMyshPl5LJHAlISM6NyQkIipicm4/KCEiKiQiMD5dQFZnWyFbISM5NyQkIjA2NjYxKFxzeCEjOiQiMVdbJkhnYmYnXCEjOjckJCIxS0xMJEcza0wpISM7JCIxLSslR1B2I3BeISM6NyQkIjEpKSkpKSkpR2drIiopISM7JCIxViV5JmY6Yj9hISM6NyQkIjE2NjY2L1BGJSohIzskIjFwa0hMTzZ3YyEjOjckJCIqVWAtKyIhIikkIjElPUlgITRfLGchIzo3JCQiMm1tbW0nZitlNSEjOyQiMXB3cS4rQ29qISM6NyQkIjJubW1tQ2hPNiIhIzskIjEzaGNcYnFmbiEjOjckJCIyeHh4RmQsVTsiISM7JCIxdSd5Wyw+ejkoISM6NyQkIjEqKSkpKSkzKilIQzchIzokIjEmZUJGYGEybCghIzo3JCQiMmJiYmJCNF9GIiEjOyQiMEooXFpSVzciKSEjOTckJCIySkxMJFsrVk04ISM7JCIxKHltay8tPHApISM6NyQkIjFBQUEtMCZvUSIhIzokIjFjLFpMaUNWIyohIzo3JCQiMkxMTCRbU09XOSEjOyQiMSkqW3pIR1YiKikqISM6NyQkIjIqKioqKipcYUkiKlwiISM7JCIxRmJ3WnQ7YjUhIzk3JCQiMSopKSkpKVFPRmM6ISM6JCIyLj5pc1xkJ0c2ISM6NyQkIjFBQUFQKVsoMzshIzokIjJ6UnhJbylSKzchIzo3JCQiMnZ4eHhVXWBtIiEjOyQiMlc0bGlxd0NHIiEjOjckJCIyd3h4RmRWVHMiISM7JCIyPSl6TVUmUklQIiEjOjckJCIyS0xMJHlKS3Y8ISM7JCIyKWZULSl6K2tYIiEjOjckJCIyVldXV2IpZkk9ISM7JCIyJSllciFbYEheOiEjOjckJCIya21tbVUueCk9ISM7JCIydiU0RCIpZXhhOyEjOjckJCIxTExMLiVwTiU+ISM6JCIyMERqPk43OnciISM6NyQkIjFMTEwzRWkoKj4hIzokIjIlR1xjPz01cT0hIzo3JCQiMm1tbW1aUncwIyEjOyQiMCNlcXIyJ3AqPiEjODckJCIxQUFBLXRjNkAhIzokIjF2a19lJVJuNiMhIzk3JCQiMm1tbW13WSJwQCEjOyQiMVBUOSpITjNEIyEjOTckJCIyWFdXJT5CS0BBISM7JCIwXCk+LWMseUIhIzg3JCQiKilST3lBISIpJCIyJjQ+aVhWUEJEISM6NyQkIjFBQUFQZC5LQiEjOiQiMi5fUyI9L0ptRSEjOjckJCIyTkxMJCk9USIpUSMhIzskIjEsTHUleWRBI0chIzk3JCQiMSopKSkpKSllKSlIVyMhIzokIjFOOSQzKTRMIilIISM5NyQkIjIoKioqKipcKD1UK0QhIzskIjJ5U0Elb0EtYkohIzo3JCQiMlpXV1dLPGRiIyEjOyQiMkV1R3ZfIVFITCEjOjckJCIyV1dXVzh2QWgjISM7JCIxLj5YIkdAXV4kISM5NyQkIjFBQUE8WU9vRSEjOiQiMTJGVFFcZzFQISM5NyQkIjFubW1FXSEqPkYhIzokIjJ2SWoxXl4kKilRISM6NyQkIjJEQUFBOncqeUYhIzskIjBjMUsmSCZvNSUhIzg3JCQiMTY2NnIrIj0kRyEjOiQiMjt5PVRTPSkzViEjOjckJCIyTkxMJFs/OSkpRyEjOyQiMUYoSHQlZi5LWCEjOTckJCIyTkxMJFEqZT8lSCEjOyQiMWxlaSIzV012JSEjOTckJCIjSSEiIiQiJCsmISIiLSUmQ09MT1JHNiYlJFJHQkckIiM1ISIiJCIiISEiIiQiIiEhIiItJSdDVVJWRVNHNiQ3UzckJCIxTExMTExMTEwhIzskITEqekFXNmdfJ3ohIzs3JCQiMXl4eHgyZjlSISM7JCExVVdMKmYuIj4nKiEjOzckJCIxQUFBcyhSLlUlISM7JCEySjwkZW9cU2s1ISM7NyQkIjE2NjY2dTUqKVwhIzskITJsYC9gP1EqUTYhIzs3JCQiMDY2NkBYO2MmISM6JCEwM1EzJW9NdDYhIzk3JCQiMSopKSkpKVE9WUpoISM7JCExeV9acmJNbzYhIzo3JCQiMVdXVyV6YShmbSEjOyQhMlU2QyZ6I2YnRzYhIzs3JCQiKmJybj8oISIqJCEyJmYiUnd5PzYwIiEjOzckJCIwNjY2MShcc3ghIzokITEoXE9Hbm5ESSohIzs3JCQiMUtMTCRHM2tMKSEjOyQhMXMpPSVSZCpIbSghIzs3JCQiMSkpKSkpKSlHZ2siKikhIzskITEwIT1pWGFMXCYhIzs3JCQiMTY2NjYvUEYlKiEjOyQhMWtgKmYlMyxbSiEjOzckJCIqVWAtKyIhIikkIjJEW3QuMSk0QDohIz43JCQiMm1tbW0nZitlNSEjOyQiMV53LEFeOiJ6JCEjOzckJCIybm1tbUNoTzYiISM7JCIxWz0lKjQvY1YhKSEjOzckJCIyeHh4RmQsVTsiISM7JCIyPWVhRW9PbUMiISM7NyQkIjEqKSkpKSkzKilIQzchIzokIjJvMiYpW1R1dCU9ISM7NyQkIjJiYmJiQjRfRiIhIzskIjA2XTBCOFhVIyEjOTckJCIySkxMJFsrVk04ISM7JCIyMXBZXkBuMD0kISM7NyQkIjFBQUEtMCZvUSIhIzokIjIvWFwkWzw9SlIhIzs3JCQiMkxMTCRbU09XOSEjOyQiMUg3cm0ieSpbWyEjOjckJCIyKioqKioqXGFJIipcIiEjOyQiMTYoPix3ejMjZSEjOjckJCIxKikpKSkpUU9GYzohIzokIjFtZyY+PjxRJXAhIzo3JCQiMUFBQVApWygzOyEjOiQiMWtUT1MsSnohKSEjOjckJCIydnh4eFVdYG0iISM7JCIxJnBYdDQsS1UqISM6NyQkIjJ3eHhGZFZUcyIhIzskIjJyS28qeiFHZTQiISM6NyQkIjJLTEwkeUpLdjwhIzskIjIkPVFScGlxVDchIzo3JCQiMlZXV1diKWZJPSEjOyQiMlJAaHQpNCNHVCIhIzo3JCQiMmttbW1VLngpPSEjOyQiMiRIZEA4T0IwOyEjOjckJCIxTExMLiVwTiU+ISM6JCIxWysxYXZzND0hIzk3JCQiMUxMTDNFaSgqPiEjOiQiMk4kXFYlUVBQLSMhIzo3JCQiMm1tbW1aUncwIyEjOyQiMS4jPWMwJSo0RyMhIzk3JCQiMUFBQS10YzZAISM6JCIxYEpBbCtySUQhIzk3JCQiMm1tbW13WSJwQCEjOyQiMjB5YkA8YXgiRyEjOjckJCIyWFdXJT5CS0BBISM7JCIyKCpvYndbb3A0JCEjOjckJCIqKVJPeUEhIikkIjFrSS0nZU1TVSQhIzk3JCQiMUFBQVBkLktCISM6JCIxbmJHWXliYFAhIzk3JCQiMk5MTCQpPVEiKVEjISM7JCIwZWNdeVE7NyUhIzg3JCQiMSopKSkpKSllKSlIVyMhIzokIjIwZCh6aS4jZl0lISM6NyQkIjIoKioqKipcKD1UK0QhIzskIjJ2KWVIdCZvXyRcISM6NyQkIjJaV1dXSzxkYiMhIzskIjFANmdeKSozd2AhIzk3JCQiMldXV1c4dkFoIyEjOyQiMm06JlskPT9lJmUhIzo3JCQiMUFBQTxZT29FISM6JCIyTmMsUF0ocGhqISM6NyQkIjFubW1FXSEqPkYhIzokIjEvUUJaI3BTJm8hIzk3JCQiMkRBQUE6dyp5RiEjOyQiMU0+dSRIPkBYKCEjOTckJCIxNjY2cisiPSRHISM6JCIwTnJqKEh1PSEpISM4NyQkIjJOTEwkWz85KSlHISM7JCIxYChcLk15cmwpISM5NyQkIjJOTEwkUSplPyVIISM7JCIxJClRNUcoUkVJKiEjOTckJCIjSSEiIiQiMiV5KnBjIjNfLjUhIzktJSZDT0xPUkc2JiUkUkdCRyQiMidcXydlTSV5Zz4hIzwkIjFpajkuZUBSISkhIzskIjInXF8nZU0leWc+ISM8LSUlVklFV0c2JDskIitMTExMTCEjNSQiI0khIiIlKERFRkFVTFRHLSUqQVhFU1NUWUxFRzYjJSdOT1JNQUxHLSUoU0NBTElOR0c2IyUuVU5DT05TVFJBSU5FREctJSVST09URzYnLSUpQk9VTkRTX1hHNiMkIiRTJCEiIi0lKUJPVU5EU19ZRzYjJCIkKyIhIiItJS1CT1VORFNfV0lEVEhHNiMkIiVJTiEiIi0lLkJPVU5EU19IRUlHSFRHNiMkIiU/TiEiIi0lKUNISUxEUkVORzYi

Part c) Find a value of t such that y(t)=10. We use the t=3 argument to tell Maple to start looking for a solution near t=3. Otherwise Maple finds a solution of about 0. tmax:=fsolve(alpha[2]=10,t=3);

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Part d) Make a plot of the trace of alpha for x>2*lambda and 0<=y<=10 plot([alpha[1],alpha[2],t=tmin..tmax]);

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Part e) Use Maple to compute the velocity and acceleration vectors for this curve. Note the use of 'map' here. In my version of Maple, diff(alpha,t) returns an error. The command map(diff,alpha,t) returns a vector such that diff(*,t) has been done to each entry of the vector. lambda:='lambda'; alphap:=map(diff,alpha,t);

SSdsYW1iZGFHNiI=

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alphapp:=map(diff,alphap,t);

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Part f) What angle does the cuve make with respect to the x-axis at x=2lambda? a0:=subs(t=1,alphap);

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a0:=a0 / (a0[1]^2+a0[2]^2)^(1/2);

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a0:=simplify(a0) assuming lambda>0;

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cos(theta)=a0[1];

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solve(%,theta);

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PROBLEM 3 Part a) See PDF file. Part b) Compute arclength over one period (assuming a=1) alpha:=<a*(t-sin(t)),a*(1-cos(t))>;

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a:=1;alphap:=map(diff,alpha,t);

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ds:=simplify(sqrt(alphap[1]^2+alphap[2]^2));

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int(ds,t=0..2*Pi);

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Part c) What happens if you try to compute the general arclength function? int(ds,t);

LCQqKiwmISIiIiIiKiQtSSRjb3NHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI2IywkSSJ0R0YtI0YmIiIjRjJGJkYmRihGJi1JJHNpbkdGKkYuRiUsJkYmRiZGJ0YlI0YlRjIiIiU=

plot(%,t=0..6*Pi);

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

Part d) Generate a plot of the arclength function over three periods. s:=Int(subs(t=u,ds),u=0..t);

LUkkSW50RzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiQqJCksJiIiIyIiIiomRixGLS1JJGNvc0dGJDYjSSJ1R0YnRi0hIiIjRi1GLEYtL0YyOyIiIUkidEdGJw==

plot(s,t=0..6*Pi);

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

TTdSMApJNFJUQUJMRV9TQVZFLzg2ODQwODRYKiUpYW55dGhpbmdHNiI2IltnbCEjJSEhISIjIiMsJComJSdsYW1iZGFHIiIiLCgqJCUidEchIiJGKkYtIiIjKiRGLSIiJEYqRiojRipGLywmKiZGKUYqLCgtJSNsbkc2I0YsRioqJEYtRi9GKiokRi0iIiUjRjFGO0YqRjJGKSMhIigiIilGJg==TTdSMApJNFJUQUJMRV9TQVZFLzg3NzMzMzZYKiUpYW55dGhpbmdHNiI2IltnbCEjJSEhISIjIiMsJComJSdsYW1iZGFHIiIiLCgqJCUidEchIiMhIiIiIiNGKiokRi1GMCIiJEYqI0YqRjAsJComRilGKiwoKiRGLUYvRi9GLUYwKiRGLUYyRjJGKkYzRiY=TTdSMApJNVJUQUJMRV9TQVZFLzExMzQyMDUyWColKWFueXRoaW5nRzYiNiJbZ2whIyUhISEiIyIjLCQqJiUnbGFtYmRhRyIiIiwmKiQlInRHISIkIiIjRi0iIidGKiNGKkYvLCQqJkYpRiosKCokRi0hIiNGKkYvRioqJEYtRi8iIipGKkYxRiY=TTdSMApJNVJUQUJMRV9TQVZFLzExMzQ2OTk2WColKWFueXRoaW5nRzYiNiJbZ2whIyUhISEiIyIjLCQlJ2xhbWJkYUciIiNGJ0YmTTdSMApJNFJUQUJMRV9TQVZFLzkzMjg0NzJYKiUpYW55dGhpbmdHNiI2IltnbCEjJSEhISIjIiMsJCooIiIpIyIiIiIiIyokJSdsYW1iZGFHRiwjISIiRixGLkYrI0YrIiIlRidGJg==TTdSMApJNFJUQUJMRV9TQVZFLzk1NTQ0MDRYKiUpYW55dGhpbmdHNiI2IltnbCEjJSEhISIjIiMsJCokIiIjIyIiIkYpRipGJ0YmTTdSMApJNVJUQUJMRV9TQVZFLzEyMTI3OTYwWColKWFueXRoaW5nRzYiNiJbZ2whIyUhISEiIyIjKiYlImFHIiIiLCYlInRHRiktJSRzaW5HNiNGKyEiIkYpKiZGKEYpLCZGKUYpLSUkY29zR0YuRi9GKUYmTTdSMApJNVJUQUJMRV9TQVZFLzEyMTE4NTc2WColKWFueXRoaW5nRzYiNiJbZ2whIyUhISEiIyIjLCYiIiJGKC0lJGNvc0c2IyUidEchIiItJSRzaW5HRitGJg==