Question

I need a python code for this problem and it should contain 9 plots.

- Problem 2: Numerical integration and differentiation Define a piece-wise continuous function (t):

Answer 1

code:

import math
def y(t): # lambda function
if t<2:
return 0
elif t>2 && t<4:
return t-2
elif t>4 && t<6:
return 2
else:
a = 2*math.exp(-(t-6))
return a

def diffy(t): # differentiation of lambda function
if t<2:
return 0
elif t>2 and t<4:
return 1
elif t>4 and t<6:
return 0
else:
a = 2*(-(t-6))*math.exp(-(t-5))
return a

def integy(t): #integration of lambda function
if t < 2:
return 0
elif t > 2 and t < 4:
return (t**2 /2 - 2*t )
elif t > 4 and t < 6:
return 2*t
else:
a = 2*math.exp(-(t-6))/(-(t-6))
return a
  

#solving question 1
import matplotlib.pyplot as plt
import numpy as np
t = np.arange(0.,16.,0.5)
acceleration = []
for i in range(len(t)):
acceleration.append(y(t[i]))
velocity = [] # integration of acceleration = integy function
for i in range(len(t)):
velocity.append(integy(t[i]))
#print(acceleration)
#print(velocity)
position1 = [a*b for a,b in zip(velocity,t)]
positiion2 = [(1/2)a(b**2) for a,b in zip(acceleration,t)]
position = [a+b for a,b in zip(position1,positiion2)]

plt.plot(t,position,c='red',ls='',marker='*')
ax = plt.gca()
ax.set_ylim([0,10])
plt.title('Position vs time')
plt.xlabel('time')
plt.ylabel('position')
plt.show()
plt.plot(t,velocity,c='red',ls='',marker='*')
ax = plt.gca()
ax.set_ylim([0,25])
plt.title('Time vs Velocity')
plt.xlabel('time')
plt.ylabel('velocity')
plt.show()
plt.plot(t,acceleration,c='red',ls='',marker='*')
ax = plt.gca()
ax.set_ylim([0,5])
plt.title('Time vs Acceleration')
plt.xlabel('time')
plt.ylabel('accaeleration')
plt.show()

#Solving question2
t = np.arange(0.,16.,0.5)
velocity = []
for i in range(len(t)):
velocity.append(y(t[i]))
acceleration= [] # integration of acceleration = integy function
for i in range(len(t)):
acceleration.append(integy(t[i]))
#print(acceleration)
#print(velocity)
position1 = [a*b for a,b in zip(velocity,t)]
positiion2 = [(1/2)a(b**2) for a,b in zip(acceleration,t)]
position = [a+b for a,b in zip(position1,positiion2)]

plt.plot(t,position,c='red',ls='',marker='*')
ax = plt.gca()
ax.set_ylim([0,500])
plt.title('Position vs time')
plt.xlabel('time')
plt.ylabel('position')
plt.show()
plt.plot(t,velocity,c='red',ls='',marker='*')
ax = plt.gca()
ax.set_ylim([0,25])
plt.title('Time vs Velocity')
plt.xlabel('time')
plt.ylabel('velocity')
plt.show()
plt.plot(t,acceleration,c='red',ls='',marker='*')
ax = plt.gca()
ax.set_ylim([0,50])
plt.title('Time vs Acceleration')
plt.xlabel('time')
plt.ylabel('accaeleration')
plt.show()

# solving question3
t = np.arange(0.,16.,0.5)
position = []
for i in range(len(t)):
position.append(y(t[i]))
velocity = [] # integration of acceleration = integy function
acceleration=[]
#print(acceleration)
#print(velocity)
acceleration= [2*(a/(t**2)) for a,b in zip(position,t)]
velocity = [2*a*b for a,b in zip(acceleration,position)]
velocity = [i**(1/2) for i in velocity]

plt.plot(t,position,c='red',ls='',marker='*')
ax = plt.gca()
ax.set_ylim([0,10])
plt.title('Position vs time')
plt.xlabel('time')
plt.ylabel('position')
plt.show()
plt.plot(t,velocity,c='red',ls='',marker='*')
ax = plt.gca()
ax.set_ylim([0,25])
plt.title('Time vs Velocity')
plt.xlabel('time')
plt.ylabel('velocity')
plt.show()
plt.plot(t,acceleration,c='red',ls='',marker='*')
ax = plt.gca()
ax.set_ylim([0,5])
plt.title('Time vs Acceleration')
plt.xlabel('time')
plt.ylabel('accaeleration')

plt.show();

SCREENSHOT;

[2]: import math def y(t): if t<2: return elif t>2 && t<4: return t-2 elif t>4 && t<6: return 2 else: a = 2*math.exp(-(t-6)) return a [10]: def diffy(t): if t 2: return elif t>2 and t<4: return 1 elif t>4 and t<6: return o else: a = 2*(-(t-6))*math.exp(-(t-5)) return a

[4]: def integy(t): if t < 2: return 0 elif t > 2 and t < 4: return (t**2 /2 - 2*t ) elif t > 4 and t < 6: return 2*t else: a = 2*math.exp(-(t-6))/(-(t-6)) return a [33]: #solving question 1 import matplotlib.pyplot as plt import numpy as np t = np.arange(0.,16.,0.5) acceleration = [] for i in range (len(t)): acceleration.append(y(t[i])) velocity = [] # integration of acceleration = integy function for i in range (len(t)): velocity.append(integy(t[i])) #print(acceleration) #print(velocity) position1 = (a*b for a,b in zip(velocity,t)] positiion2 = [(1/2)*a*(b**2) for a,b in zip(acceleration, t)]

positiion2 = [(1/2)*a*(b**2) for a,b in zip(acceleration, t)] position = [a+b for a,b in zip(positioni, positiion2)] plt.plot(t, position, c='red', 1s=',marker='*') ax = plt.gca() ax.set_ylim([0,10]) plt.title('Position vs time') plt.xlabel('time') plt.ylabel('position') plt.show() plt.plot(t,velocity,c='red', 1s='',marker='*') ax = plt.gca() ax.set_ylim([0,25]) plt.title('Time vs Velocity') plt.xlabel('time') plt.ylabel('velocity') plt.show() plt.plot(t, acceleration, c='red', 1s='',marker='*') ax = plt.gca() ax.set_ylim([0,5]) plt.title('Time vs Acceleration') plt.xlabel('time') plt.ylabel('accaeleration') plt.show()

Position vs time position O À 6 5 10 12 14 16 time

Time vs Velocity velocity 10 12 14 16 8 time

Time vs Acceleration accaeleration 2 4 6 8 time 10 12 14 16 [39]: #Solving question2 t = np.arange (0., 16.,0.5) velocity = [] for i in range (len(t)): velocity.append(y(t[i])) acceleration= [] # integration of acceleration = integy function for i in range (len(t)): acceleration.append(integy(t[i])) #print(acceleration)

TPI LILI UCCELEIUL LUI #print(velocity) position1 = [a*b for a,b in zip(velocity,t)] positiion2 = [(1/2)*a*(b**2) for a,b in zip(acceleration, t)] position = [a+b for a,b in zip(positioni, positiion2)] plt.plot(t, position,c='red', 1s='', marker='*') ax = plt.gca) ax.set_ylim([0,500]) plt.title('Position vs time') plt.xlabel('time') plt.ylabel('position') plt.show() plt.plot(t, velocity,c='red', 1s='',marker='*') ax = plt.gca() ax.set_ylim([0,25]) plt.title('Time vs Velocity') plt.xlabel('time') plt.ylabel('velocity') plt.show() plt.plot(t, acceleration, c='red', 1s='',marker='*') ax = plt.gca() ax.set_ylim([0,50]) plt.title('Time vs Acceleration') plt.xlabel('time') plt.ylabel('accaeleration') plt.show

Position vs time position OL+ 02 2 4 6 8 time 10 12 14 16

IU time Time vs Velocity velocity 5 1 6 8 time 10 12 14 16

Time vs Acceleration accaeleration 00 À 681021416 time [42]: # solving question3 t = np.arange(0.,16., 0.5) position = [] for i in range(len(t)): position.append(y(t[i])) velocity = [] # integration of acceleration = integy function acceleration=[] #print(acceleration) #print(velocity) acceleration= [2*(a/(t**2)) for a,b in zip(position, t)]

acceleration= [2*(a){t**2)) for a, b in zip position,t)] velocity = [2*a*b for a, b in zip(acceleration, position)] velocity = [i**(1/2) for i in velocity] plt.plot(t, position,c='red', 1s='', marker='*') ax = plt.gca() ax.set_ylim([0,10]) plt.title('Position vs time') plt.xlabel('time') plt.ylabel('position') plt.show() plt.plot(t, velocity,c='red', 1s='', marker='*') ax = plt.gca() ax.set_ylim([0,25]) plt.title('Time vs Velocity') plt.xlabel('time') plt.ylabel('velocity') plt.show() plt.plot(t, acceleration, c='red', 1s='', marker='*') ax = plt.gca() ax.set_ylim([0,5]) plt.title('Time vs Acceleration') plt.xlabel('time') pit.ylabel('accaeleration')

Position vs time position 4 6 § 10 12 14 16 time

Time vs Velocity velocity 8 10 12 14 16 time

Time vs Acceleration accaeleration 10 12 14 16 68 time