Academic Integrity: tutoring, explanations, and feedback — we don’t complete graded work or submit on a student’s behalf.

%253Cp%2520id%253D%2522yui_3_7_3_2_1394943026679_79%2522%2520class%253D%2522c2%2

ID: 3896738 • Letter: #

Question

%253Cp%2520id%253D%2522yui_3_7_3_2_1394943026679_79%2522%2520class%253D%2522c2%2522%253EA%2520light%2520rod%2520of%250Alength%25201.8%2520m%2520has%2520two%2520point%2520masses%2520of%2520mass%25202%2520kg%2520attached%2520at%2520either%250Aend.%2520The%2520rod%2520is%2520pivoted%2520about%2520its%2520centre%2520and%2520is%2520attached%2520to%2520a%250Aspring%2520which%2520exerts%2520a%2520moment%2520on%2520the%2520rod%2520that%2520is%2520proportional%2520to%2520the%250Aangle%2520the%2520rod%2520is%2520displaced%2520from%2520the%2520equilibrium%2520position%2520and%2520which%250Aattempts%2520to%2520return%2520the%2520rod%2520to%2520the%2520equilibrium%2520position.%2520The%2520rod%2520is%250Adisplaced%25200.08%2520rad%2520from%2520the%2520equilibrium%2520position%2520and%2520released%2520from%250Arest.%2520If%2520the%2520spring%2520constant%2520is%25203.7%2520Nm.rad%253Csup%2520class%253D%250A%2522c1%2522%253E-1%253C%252Fsup%253E%2520what%2520is%2520the%2520period%2520of%2520the%2520resulting%2520motion%253F%253C%252Fp%253E%250A%253Cp%2520class%253D%2522c2%2522%253E%255BNote%253A%2520A%2520moment%252C%2520or%2520more%2520fully%2520a%2520moment%2520of%2520a%2520force%252C%250Ais%2520sometimes%2520called%2520a%2520torque%2520by%2520engineers%2520and%2520those%2520in%2520the%2520US%250A(which%2520is%2520where%2520your%2520textbook%2520was%2520printed).%255D%253C%252Fp%253E%250A

Explanation / Answer

Moment of Inertia = 2* [m*l*l/3] ; l = 1.8/2

MOI = 1.08 kg.m2


For this, the natural frequency, omega, w is given by sqrt(K/MOI)


w = sqrt(3.7/1.08) = 1.85 rad/sec