Create a free account and view content that fits your specific interests in structural engineering Learn More
This calculation is an example problem in structural engineering. This content is sponsored by PPI. For similar problems, see the list of review books by PPI
A single point with mass m is vibrating harmonically. The displacement x from point of balance is governed by the differential equation
where ω is a positive constant.
a) Show that
and
are equivalent.
Solution
So the form is x(t)=A sinωt+B cosωt
where
x(t)=A sinωt+B cosωt
with
See a complete list of review books with similar examples.
Selected Topics
Calculation Example: Natural Periods of Vibration for SystemsCalculation Example: Axial Force On A ColumnCalculation Example: Shear force On A ColumnCalculation Example: Overturning Moment for Shear panelCalculation Example: Calculate the Change in Length of a Rod loaded in extensionCalculation Example - Calculate the Axial Forces on the Truss MembersCalculation Example - Calculate the member diagramsCalculation Example - Calculate the member diagrams for the beamCalculation Example – Beam with inner hinge (Part A). Find the ReactionsCalculation Example – Beam with inner hinge (Part B). Calculate the member diagrams.Calculation Example – Frame analysis.Calculation Example – Frame analysis – Uniform LoadCalculation Example – Find the Center of Gravity (Surface)Calculation Example – Design bolted connection of tension plates (EC3)Calculation Example – Cantilever BeamCalculation Example – Cantilever Beam, Temperature changeCalculation Example – Undamped free Vibration (Part A).Calculation Example – Undamped free Vibration (Part B).Calculation Example – Evaluation of Structural Property Matrices.Calculation Example – Angular acceleration, angular velocity.Calculation Example – Shear bolt connection EC3.Calculation Example – Buckling of Column (EC3).Calculation Example - Calculate the member diagrams.Calculation Example - Calculate the member diagrams.Calculation Example - Calculate the equation of the elastic curve.Calculation Example - Calculate the location of support.Calculation Example – Plane stress.Calculation Example - Annular cross section, Stress.Calculation Example – Allowable shear force for the girder.Calculation Example - Calculate the deflection. Castigliano Theorem.Calculation Example – Determine the shear force and moment.Calculation Example – Determine the magnitudes of F1,F2.Calculation Example – Internal forces.Calculation Example - Calculate the Axial Forces of the Truss Members.Calculation Example – Calculate the moments of inertia Ix and Iy.Calculation Example – Calculate shear stress for temperature load.Calculation Example – Calculate tension force using virtual work.Calculation Example – Torsional moment-Stress.Calculation Example – Reinforced Concrete Column at Stress.Calculation Example – Cantilever Beam with uniform loading.Calculation Example – Cantilever Beam with point loads.Calculation Example – Rod loadingCalculation Example – Maximum DeflectionCalculation Example – Member Diagram.Calculation Example – Minimum allowable Diameter.Calculation Example – Critical load.Calculation Example – Simple harmonic vibration part 2Calculation Example – FrictionCalculation Example – Section Modulus SCalculation Example – Plastic Neutral Axis.Calculation Example – Buckling of Column (EC3).Calculation Example – Shear bolt connection EC3.Calculation Example – Member Diagram. Triangular load.Calculation Example – Torsional moment-Stress.Calculation Example – Angular acceleration, angular velocity.Calculate the location of point loadShear bolt connection EC3Torsional Moment-StressCalculate the Axial Forces of the Truss MembersCalculate the Maximum Shear StressHow to calculate yield strengthCalculate angular velocity, angular accelerationTemperature ChangeAverage shear stress in pressure vesselAllowable shear force of the girderCalculation Examples
See Also
Calculation Examples
Feb, 13, 2020_
Professional Examinations Preparation
Feb, 13, 2020
Allowable shear force of the girder
Jan, 15, 2020Calculate the maximum allowable shear force Vmax...
Average shear stress in pressure vessel
Nov, 04, 2019A pressure-vessel head is fabricated by gluing the...
Temperature Change
Sep, 30, 2019The beam is fixed at end B and free at end A. It i...
Calculate angular velocity, angular acceleration
Sep, 09, 2019The angular velocity of the circle is defined by t...
