A.8.5: Section 8.5 Answers
- Last updated
- Jun 8, 2024
- Save as PDF
( \newcommand{\kernel}{\mathrm{null}\,}\)
1. y=3(1−cost)−3u(t−π)(1+cost)
2. y=3−2cost+2u(t−4)(t−4−sin(t−4))
3. y=−152+32e2t−2t+u(t−1)2(e2(t−1)−2t+1)
4. y=12et+136e−t+13e2t+u(t−2)(−1+12et−2+12e−(t−2)+12et+2−16e−(t−6)−13e2t)
5. y=−7et+4e2t+u(t−1)(12−et−1+12e2(t−1))−2u(t−2)(12−et−2+12e2(t−2))
6. y=13sin2t−3cos2t+13sint−2u(t−π)(13sint+16sin2t)+u(t−2π)(13sint−16sin2t)
7. y=14−3112e4t+163et+u(t−1)(23et−1−16e4(t−1)−12)+u(t−2)(14+112e4(t−2)−13et−2)
8. y=18(cost−cos3t)−18u(y−3π2)(sint−cost+sin3t−13cos3t)
9. y=t4−18sin2t+18u(t−π2)(πcos2t−sin2t+2π−2t)
10. y=t−sint−2u(t−π)(t+sint+πcost)
11. y=u(t−2)(t−12+e2(t−2)2−2et−2)
12. y=t+sint+cost−u(t−2π)(3t−3sint−6πcost)
13. y=12+12e−2t−e−t+u(t−2)(2e−(t−2)−e−2(t−2)−1)
14. y=−13−16e3t+12et+u(t−1)(23+13e3(t−1)−et−1)
15. y=14(et+e−t(11+6t))+u(t−1)(te−(t−1)−1)
16. y=et−e−t−2te−t−u(t−1)(et−e−(t−2)−2(t−1)e−(t−2))
17. y=te−t+e−2t+u(t−1)(e−t(2−t)−e−(2t−1))
18. y=t2e2t2−te2t−u(t−2)(t−2)2e2t
19. y=t412+1−112u(t−1)(t4+2t3−10t+7)+16u(t−2)(2t3+3t2−36t+44)
20. y=12e−t(3cost+sint)+12−u(t−2π)(e−(t−2π)((π−1)cost+2π−12sint)+1−t2)−12u(t−3π)(e−(t−3π)(3πcost+(3π+1)sint)+t)
21. y=t22+∑∞m=1u(t−m)(t−m)22
22.
- y={2m+1−cost,2mπ≤t<(2m+1)π(m=0,1,…)2m,(2m−1)π≤t<2mπ(m=1,2,…)
- y=(m+1)(t−sint−mπcost),2mπ≤t<(2m+2)π(m=0,1,…)
- y=(−1)m−(2m+1)cost,mπ≤t<(m+1)π(m=0,1,…)
- y=em+1−12(e−1)(et−m+e−t)−m−1,m≤t<m+1(m=0,1,…)
- y=(m+1−(e2(m+1)π−1e2π−1)e−t)sint2mπ≤t<2(m+1)π(m=0,1,…)
- y=m+12−et−mem+1−1e−1+12e2(t−m)e2m+2−1e2−1,m≤t<m+1(m=0,1,…)
