Apply Laplace transform properties to determine the Laplace transform of the following functions
Consider a linear time invariant (LTI) system of Figure Q2. Given that the input of the system X(s) is a unit step function and the output Y(s) of the system is described by the following expression:
Figure Q2
Determine the following characteristics of the LTI system:
The transfer function H(s). [4 Marks]
The output response y(t) for an input signal x(t) = 5t u(t).[8 Marks]
The inverse Laplace transforms of [8 Marks]
Consider the causal continues-time LTI system characterized by the following differential equation
(i)Use Laplace transform method to determine the poles, zeroes, region of the convergence (ROC) and the output response y(t) of the system.[14 Marks]
Sketch the pole-zero pattern of and its ROC.[6 Marks]
Sample Solution
The outbreak of Indo-Pak war on 6 September 1965 constituted a major test of the friendship of Pakistanâs regional allies. The Turkish Premier, Mr. Urugplu said that the Turkish government hoped that efforts by UN Secretary General U Thant to achieve a ceasefire would prove successful. He also said that India had aggravated the crises by taking the conflict beyond Kashmir into Pakistan and by bombing Pakistani Towns. He further observed: âThe dangerous crisis which has been developing recently between the two countries is a direct result of the failure in finding a just solution to the Kashmir Problems.â On 10 September 1965, Turkey and Iran in a joint statement called for an immediate ceasefire, the withdrawal of Indian forces from Pakistani territory. The communiqu?? concluded: âthe Governments of turkey and Iran reaffirmed the solidarity which links Turkey-Iran and Pakistan, and declared that they are ready to support Pakistan as a brother country and an ally (Ali, 2001). The Turkish Premier announced that Turkey would send five million dollarsâ worth of Turkish made arms and ammunition to Pakistan under the terms of an existing trade agreement. Though Turkey could not respond to favorably to Pakistanâs appeal for Jet aircraft , presumably because the US would have objected to the transfer of material which she had given , Turkey decided to âuse all national possibilities , to aid Pakistan with guns and ammunition. Large numbers of Turks volunteered to fight against India and a number of Nurses flew to Pakistan and served there (Burke, 1973). Pakistan was deeply touched by the Turkeyâs sympathetic attitude and President Ayub visited Turkey in December 1965 and met president Cemal Gursal. He>
The outbreak of Indo-Pak war on 6 September 1965 constituted a major test of the friendship of Pakistanâs regional allies. The Turkish Premier, Mr. Urugplu said that the Turkish government hoped that efforts by UN Secretary General U Thant to achieve a ceasefire would prove successful. He also said that India had aggravated the crises by taking the conflict beyond Kashmir into Pakistan and by bombing Pakistani Towns. He further observed: âThe dangerous crisis which has been developing recently between the two countries is a direct result of the failure in finding a just solution to the Kashmir Problems.â On 10 September 1965, Turkey and Iran in a joint statement called for an immediate ceasefire, the withdrawal of Indian forces from Pakistani territory. The communiqu?? concluded: âthe Governments of turkey and Iran reaffirmed the solidarity which links Turkey-Iran and Pakistan, and declared that they are ready to support Pakistan as a brother country and an ally (Ali, 2001). The Turkish Premier announced that Turkey would send five million dollarsâ worth of Turkish made arms and ammunition to Pakistan under the terms of an existing trade agreement. Though Turkey could not respond to favorably to Pakistanâs appeal for Jet aircraft , presumably because the US would have objected to the transfer of material which she had given , Turkey decided to âuse all national possibilities , to aid Pakistan with guns and ammunition. Large numbers of Turks volunteered to fight against India and a number of Nurses flew to Pakistan and served there (Burke, 1973). Pakistan was deeply touched by the Turkeyâs sympathetic attitude and President Ayub visited Turkey in December 1965 and met president Cemal Gursal. He>
