Exam (elaborations)
SME3701 Minor Test 2 Answers Year 2024
- Course
- Institution
Distinction Guaranteed
[Show more]
Seller
Follow
TrustAcademy
Reviews received
Content preview
Solid Mechanics IVMinor Test 2 Answers
Year 2024
20 SEPTEMBER 2024
DUE DATE
,
, QUESTION 1
k = 4 000 N/m m = 10 kg c = 30 N.s/m F(t) = 200 cos 12t
𝐹0 = 200 𝑁 𝜔 = 12 𝑟𝑎𝑑/𝑠 𝑥0 = 0.1 𝑥̇ 0 = 0
𝑘 4 000
𝜔𝑛 = √ = √ = 20 𝑟𝑎𝑑/𝑠
𝑚 10
𝐹0 200
𝛿𝑠𝑡 = = = 0.05 𝑚
𝑘 4 000
𝑐 𝑐 30
𝜁= = = = 0.075
𝑐𝑐 2√𝑘𝑚 2√(4000)(10)
𝜔𝑑 = √1 − 𝜁 2 . 𝜔𝑛 = √1 − 0.0752 × 20 = 19.943671 𝑟𝑎𝑑/𝑠
𝜔 12
𝑟= = = 0.6
𝜔𝑛 20
𝛿𝑠𝑡 0.05
𝑋= =
√(1 − 𝑟 2 )2 + (2𝜁𝑟)2 √(1 − 0.62 )2 + ((2)(0.075)(0.6))
2
= 0.077364
2𝜁𝑟 2 × 0.075 × 0.6
𝜙 = 𝑎𝑟𝑐𝑡𝑎𝑛 ( 2
) = arctan ( )
1−𝑟 1 − 0.62
= 0.139709 𝑟𝑎𝑑
Steady state response:
𝑥𝑝 (𝑡) = 𝑋 cos(𝜔𝑡 − 𝜙)
𝒙𝒑 (𝒕) = 𝟎. 𝟎𝟕𝟕𝟑𝟔𝟒 𝐜𝐨𝐬(𝟏𝟐𝒕 − 𝟎. 𝟏𝟑𝟗𝟕𝟎𝟗)
The benefits of buying summaries with Stuvia:
Guaranteed quality through customer reviews
Stuvia customers have reviewed more than 700,000 summaries. This how you know that you are buying the best documents.
Quick and easy check-out
You can quickly pay through credit card or Stuvia-credit for the summaries. There is no membership needed.
Focus on what matters
Your fellow students write the study notes themselves, which is why the documents are always reliable and up-to-date. This ensures you quickly get to the core!
Frequently asked questions
What do I get when I buy this document?
You get a PDF, available immediately after your purchase. The purchased document is accessible anytime, anywhere and indefinitely through your profile.
Satisfaction guarantee: how does it work?
Our satisfaction guarantee ensures that you always find a study document that suits you well. You fill out a form, and our customer service team takes care of the rest.
Who am I buying these notes from?
Stuvia is a marketplace, so you are not buying this document from us, but from seller TrustAcademy. Stuvia facilitates payment to the seller.
Will I be stuck with a subscription?
No, you only buy these notes for $8.61. You're not tied to anything after your purchase.
Can Stuvia be trusted?
4.6 stars on Google & Trustpilot (+1000 reviews)
75323 documents were sold in the last 30 days
Founded in 2010, the go-to place to buy study notes for 14 years now