To understand how the two standard ways to write the general solution to a harmonic oscillator are related. there are two common forms for the general solution for the position of a harmonic oscillator as a function of time t: x(t)=acos(ωt+ϕ) andx(t)=ccos(ωt)+ssin(ωt).either of these equations is a general solution of a second-order differential equation (f⃗ =ma⃗ ); hence both must have at least two--arbitrary constants--parameters that can be adjusted to fit the solution to the particular motion at hand. (some texts refer to these arbitrary constants as boundary values.)a)find analytic expressions for the arbitrary constants c and s in equation 2 (found in part b) in terms of the constants a and ϕ in equation 1 (found in part a), which are now considered as given parameters. give your answers for the coefficients of cos(ωt) and sin(ωt), separated by a comma. express your answers in terms of a and ϕ.

Why is metal often used for cooking pan?

Clothing made of several thin layers of fabric with trapped air in between, often called ski clothing, is commonly used in cold climates because it is light, fashionable, and a very effective thermal insulator. so it is no surprise that such clothing has largely replaced thickand heavy old-fashioned coats. (a) consider a jacket made of five layers of 0.1-mm-thick synthetic fabric (k = 0.13 w/m·°c) with 1.5-mm-thick air space (k = 0.026 w/m·°c) between the layers. assuming the inner surface temperature of the jacket to be 28°c and the surface area to be 1.25 m2, determine the rate of heat loss through the jacket when the temperature of the outdoors is 0°c and the heat transfer coefficient at the outer surface is 25 w/m2·°c. (b) what would your response be if the jacket is made of a single layer of 0.5-mm-thick synthetic fabric? what should be the thickness of a wool fabric (k = 0.035 w/m·°c) if the person is to achieve the same level of thermal comfort wearing a thick wool coat instead of a five-layer ski jacket?

Explain the comparisons between nature and packingtown that appears on pages 81 and 82 answer