Question:
For each of the following functions representing displacements find the Laplace transform, simplifying your answer as far as possible:
![](https://static.wixstatic.com/media/20c892_10372c185106459b864ee4a774992394~mv2.png/v1/fill/w_65,h_14,al_c,q_85,usm_0.66_1.00_0.01,blur_2,enc_auto/20c892_10372c185106459b864ee4a774992394~mv2.png)
Answer:
![](https://static.wixstatic.com/media/20c892_2626de84eb0843648cb93d032c92213c~mv2.png/v1/fill/w_49,h_22,al_c,q_85,usm_0.66_1.00_0.01,blur_2,enc_auto/20c892_2626de84eb0843648cb93d032c92213c~mv2.png)
![](https://static.wixstatic.com/media/20c892_fa49d65bb17c455a8c7bb6839cd09e2f~mv2.png/v1/fill/w_49,h_17,al_c,q_85,usm_0.66_1.00_0.01,blur_2,enc_auto/20c892_fa49d65bb17c455a8c7bb6839cd09e2f~mv2.png)
Alternatively, you can utilise the first shift theorem. You are able to ignore functions of e using this theorem and decrease the complexity of work. See below...
![](https://static.wixstatic.com/media/20c892_0fcc405f6fac4e539a55426d40c1f2c1~mv2.png/v1/fill/w_49,h_22,al_c,q_85,usm_0.66_1.00_0.01,blur_2,enc_auto/20c892_0fcc405f6fac4e539a55426d40c1f2c1~mv2.png)
You see we arrive at the same answer without the complexity of performing a Laplace transform on e.
![](https://static.wixstatic.com/media/20c892_03a2c1b9ece44d18a79b6c05470dd9d2~mv2.png/v1/fill/w_49,h_21,al_c,q_85,usm_0.66_1.00_0.01,blur_2,enc_auto/20c892_03a2c1b9ece44d18a79b6c05470dd9d2~mv2.png)
![](https://static.wixstatic.com/media/20c892_3e6f195848c249b695dd27165b610038~mv2.png/v1/fill/w_49,h_21,al_c,q_85,usm_0.66_1.00_0.01,blur_2,enc_auto/20c892_3e6f195848c249b695dd27165b610038~mv2.png)