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Using the trigonometric identity:. [sin A times sin B = frac{{cos (A - B) - cos (A B)}}{2}]. ... vib}}}})t) - frac{{{alpha _0}{E_0}}}{2}cos (2pi ({upsilon _{rm{p}}} {nu _{{rm{vib}}}})t)].

left| {Os} right| = ) (frac{{2cos theta }}{{sin theta }}). (left| {qr} right| = ) (frac{1}{{tan theta }}) = (frac{{cos theta }}{{sin theta }}). Lengths in drawing of indent: (QR = SO =) (frac{b}{2}). (OR = ... kb ) (left{ {frac{1}{{sin theta cos theta }}

Notched bar in tension. • Notched bar in tension. The plane strain condition is satisfied when breath, b » h, the depth of the bar. ... Let displacement along shear plane AB = δx. Then internal work done = ( {k.left| {AB} right|bdelta x} = ksqrt 2

kern 1pt} 2}}}left{ {{{sin }2}frac{alpha }{2} - 2frac{alpha }{2}cos frac{alpha }{2}sin frac{alpha }{2}} right}). = ... cos {raise0.5exhbox{$scriptstyle alpha $} kern-0.1em/kern-0.15em lower0.25exhbox{$scriptstyle 2$}}}} = {raise0.7exhbox{$1$}!

So,. $$left| {{bf{a}}} right| = {1 over {{d_{100}}}} = {1 over {left| {bf{a}} right|cos (gamma - {pi over 2})}}$$ and $${{{bf{a}}} over {left| {{bf{a}}} right|}} = ... b}} times {bf{c}}} over {left| {{bf{b}} times {bf{c}}} right|}}$$.

The scattering density of two infinitely narrow slits separated by spacing b can be described using delta functions:. ... rm{i}}{{{bf{x}}sin 2theta } over lambda }} right){rm{d}}x} cr & {rm{ = 2}}{{rm{A}}_0}cos left( {{{pi b sin 2theta } over lambda }}

B and A are initially at (cos φ', sin φ', 0) and (cos (φ' 60), sin (φ' 60), 0) respectively, while D is initially at. [ ... varphi ' 30circ ) frac{{sqrt 2 }}{{sqrt 3 }}cos theta } right){rm{ }} ]. respectively. The projection of D onto the (hat x ) -

Using the trigonometric identity:. [sin A times sin B = frac{{cos (A - B) - cos (A B)}}{2}]. ... vib}}}})t) - frac{{{alpha _0}{E_0}}}{2}cos (2pi ({upsilon _{rm{p}}} {nu _{{rm{vib}}}})t)].

left| {Os} right| = ) (frac{{2cos theta }}{{sin theta }}). (left| {qr} right| = ) (frac{1}{{tan theta }}) = (frac{{cos theta }}{{sin theta }}). Lengths in drawing of indent: (QR = SO =) (frac{b}{2}). (OR = ... kb ) (left{ {frac{1}{{sin theta cos theta }}

So,. $$left| {{bf{a}}} right| = {1 over {{d_{100}}}} = {1 over {left| {bf{a}} right|cos (gamma - {pi over 2})}}$$ and $${{{bf{a}}} over {left| {{bf{a}}} right|}} = ... b}} times {bf{c}}} over {left| {{bf{b}} times {bf{c}}} right|}}$$.